The second definition in JoeBright's answer is correct: thot is an acronym that stands for "That Ho Over There." The word has a negative connotation and is such sometimes used as an affectionate insult to close friends, but is almost always used to describe women. Ho is commonly misspelled as hoe, but intended as a short form for whore. It's generally considered AAVE, with multiple examples in hip-hop culture.
Unlike in the case of YOLO, where Drake's song "The Motto" popularised it, there seems to be no single event. Rather, the word rose to popularity gradually.
This is going to be long...
I did find a song called "Thot Walk," performed by artists John Boy, Kayleb, and Yung Cyph, but it was made after thot reached its peak popularity on Twitter. (It did start a trend on Vine, but that's another story.)
Examples of characteristics the song states are typically attributed to a thot: (couldn't find lyrics, all by ear):
0:32 "Showing off her body on her Instagram / just to get a hundred Likes on her picture"
So desperate for attention is this thot that she dresses as provocatively as possible to attract as many Likes as possible, most of which come from heterosexual men (for reasons which should be obvious).
0:40 "Got no face, but all body"
She has a body considered by society to be physically attractive (large breasts & butt, most likely) yet her face is unattractive. This may be because she has an awkward bone structure, is unkempt with her appearance, or is unskilled at applying makeup in a flattering fashion.
0:43 "Go it girl, twerk it, make a movie / If you ain't going to do it for me, do it for the Vine"
It's common on Vine for users to share videos of themselves or others twerking. Since some can even experience their 15 minutes of viral video fame as a result of a twerk Vine, the phrase do it for the Vine has leverage in persuading someone to do anything they wouldn't normally do (not just twerking) for the sake of humour or interest. I believe, however, that Kayleb is using the phrase with thinly-veiled condescension, thinking of girls who twerk for Vines as gullible or attention-seeking.
2:26 "If you one of the thots in the VIP / You'd have fucked the promoter, you don't need no ID"
Those in the VIP section of a club are there most likely either because they have money, fame, or connections to someone associated with the club. John Boy implies that having sexual relations with the promoter is a cheap or dishonest way of getting in.
2:32 "She act like a hooker with a cup full of liquor"
Once under the influence of alcohol, a thot will become promiscuous (or exchange sexual services for money, I wasn't sure).
Along with the concrete examples of thot behaviour, these two lines may also be of interest.
1:21 "She a thot so she talk like one / She a thot so she walk like one"
2:20 "You can tell she a thot by the way that she stands"
These two phrases, both without followup, suggest that there is more to being a thot than just simply being promiscuous. Part of being a thot has to do with how one carries oneself - perhaps speech patterns, lexicon, gait, posture, and/or body language are all variables in determining whether someone is a thot.
I've also searched up the word on Twitter to see how it'd be used in context, and while I did see a few instances of it being used as a shortening of thought as GEdgar suggested, those were well in the minority.
It is illogical to discard a diamond and replace it with a rock because of the drop in value: by analogy, a thot has much lower value than a wife.
Birds of a feather flock together.
Thot was clearly being used as an untrue allegation to save face publicly.
Also provides evidence to suggest that a thot carries herself differently. Presumably, a woman who "runs game" could very well also be promiscuous, but carries herself in such a way that earns her respect, reverence, or unrequited love.
I can assume from this tweet that the scenario in which a girl previously perceived as beautiful becomes a thot is common. The user laments because he believes becoming a thot is shameful.
An exception to the rule: Previously used only by men toward women, this is a woman not wanting to associate herself with anything having to do with thots.
As previously stated, a thot is most definitely promiscuous, but considering the evidence, one can start to form a profile.
A thot is well-connected on social media, but most likely has received most of her attention from desperate heterosexual men hoping to get an easy lay. Unattractive with a sense of grandeur, or perhaps attractive only with makeup, she barely only looks good enough to attract this attention. She is shameless, dishonest, or not self-aware, with further personal boundaries than most. There are a wide variety of men with whom she is willing to sustain a sexual relationship, reoccuring or not. She twerks, or does any other activity notorious for being a blatantly sexual way of attracting attention. She is a common enough occurrence for her value to have diminished. Her behaviour would be unsuitable in polite company. She befriends other thots, while other women who see themselves as better do not wish to associate with her.
Also, that ho over there is a phrase that puts physical distance between the narrator and the ho. Extrapolating, it could imply disinterest or detachment, as if the narrator knows there will be another ho over there, and over there, and over there.
And that's a thot.
The social implications of the word and its usage are a whole other can of worms, and out of the scope of this site.
Best Answer
What '[on] fleek' means and where it came from: the standard view
As Matt Эллен notes in his answer, the road to mass adoption of fleek runs through a Vine mini-video uploaded on June 21, 2014, by Peaches Monroee. If you don't have Flash on your computer (as I don't), you can relive Ms. Monroee's 12 seconds of stardom here on YouTube. One commenter at YouTube conveniently transcribes the audio of the mini-video as follows:
The suburban, red-state translation is roughly this:
A number of websites have dedicated articles to answering the two-headed question, What does fleek mean, and where does it come from? The nature of the Internet being what is (namely, a big echo chamber), most of the most heavily trafficked articles reach very similar conclusions. From Know Your Meme ("Eyebrows on Fleek"):
Know Your Meme doesn't hazard an opinion of its own about what "on fleek" means, but by way of context it notes that Peaches Monroee uses her Vine mini-video "to show off her stylishly groomed eyebrows." Clearly, "on fleek" is a good thing.
From Four-Pins.com "Twitter On Fleek: Corporate Memes, Joke Attribution And The Life Cycle of Cool," October 8, 2014):
From Racked.com ("A Brief History of Fleek, From Taco Bell to Kim Kardashian," November 5, 2014):
From Uptown Magazine ("Trademarks on Fleek: Who Owns the Word?," November 18, 2014):
Unfortunately for the Uptown Magazine author, the instance of "fleek" in the cited 1801 edition of Langhorne & Langhorne's translation of Plutarch's Lives is in fact an instance of "ſleek"—that is, "sleek"—which the author could have confirmed with a quick trip to Google Books search (the occurrence of "theſe" two words earlier and of "Caſſius" 18 words later would have provided useful clues as to what was going on with "ſleek"). I'm also at a loss to explain why the author considers 1801 to belong to "the 1st Century."
From Billboard ("From 'Pulling a Beyonce' to 'On Fleek,' Slang Terms That Invaded 2014," December 12, 2014):
From Betches Loves This ("On Fleek: Betchy Linguistics," December 22, 2014):
From Bustle ("What Does "On Fleek" Mean? A Brief Timeline of the Phrase that No One Really Understands, But Everyone Keeps Saying Anyway," December 29, 2014):
Source theory #1: 'Fleek' ultimately derives from an Urban Dictionary definition posted in 2003
Here is the famous entry for fleek posted by Dan Blue on Urban Dictionary on October 2, 2003:
The first thing you may notice about this definition is that it uses fleek as an adjective—not as a noun, and not in tandem with on. The next thing you may notice is that it is not alone. Aside from a small landslide of post–June 21, 2014 offerings, UD enthusiasts have suggested an array of definitions for fleek over the years. One of these, posted by Alycyn on December 1, 2009, might be seen as a missing link between Dan Blue's 2003 definition and Peaches Monroee's 2014 usage:
But you'll also see a gaggle of less promising entries on UD. For example, posted by AKJenk on July 4, 2005:
And posted by xxreptarlampxx on December 7, 2010, we have this:
And posted by birthmas on December 11, 2010, we have this:
Not to mention inane definitions for Fleeke (from January 23, 2008), fleeked (from October 19, 2006), and fleeko (from January 11, 2011), along with another "awesomeness"-related word, fleeky, posted on August 3, 2007:
A competing definition of fleeky posted on January 21, 2012, however, asserts that "fleeky is an onomonopia name, it is what it sounds like it. the name was created by a musician named 0110 who was apart of an experiment music group called Communion in 1996 somewhere in the east coast of the U.S.A. "
It is interesting that three of these definitions involve positives ranging from "smooth, nice, sweet" to "awesome"—but before I took that as strong evidence that Dan Blue and Alycyn were talking about the same fleek that Peaches Monroee was, I'd want to know how many of the thousands of imaginary words posted on UD also allegedly mean "awesome." I note, for example, that a poster on July 12, 2011, claims that Flege means "A person who is extremely awesome, amazing and beastly"; a poster on February 16, 2008, reports that fleischut means "amazing or the best thing ever in the whole world"; and a poster on April 13, 2008, reports that flemmin means "cool, rad, or awesome."
Ultimately, Urban Dictionary is so full of random inventions that it is impossible to tell whether a definition offered eleven years ago that happens to be reasonably close to the current definition of a word spelled the same way has any ancestral connection to the current word. At least with regard to fleek 2003 and fleek today, I'm skeptical. And if the two are directly related, that information doesn't bring us any closer to an understanding of why fleek was used in the first place.
Source theory #2: 'Fleek' is a variant of 'flick'
From PopSugar ("Eyebrows on Fleek Were the Biggest Beauty Trend of 2014," December 27, 2014):
Well, this is different. The PopSugar author says that makeup-lovers are very familiar with the word flick—so I suppose that the way to test her assertion is to look for instances where flick comes up in the context of cosmetics and try to nail down a definition of the term.
One of the first things I discovered in pursuing this question was that flick is indeed a common term used in connection with eyeliner. One online tutorial promises to show you how to perfect your "feline flick" for cat eye makeup; another article reveals "7 Hints for Creating the Perfect Eyeliner Flick." In fact, dozens of sites discuss the "flick," which refers to the "winged eyeliner" marks on the outer edge of each eye—a less exaggerated version of the eye makeup style that Amy Winehouse used to sport.
But these flicks involve the eyelashes and eyelid, not the eyebrow. A Google search did lead me to a few interesting references to "eyebrow flicks." One is from "Eyebrow Lift" at Skin Beautiful Medical & Cosmetic Clinic:
It seems highly unlikely, though, that Peaches Monroee was discussing an advanced nonsurgical procedure that she had done on her eyebrows at a cosmetology clinic.
Another mention occurs in Laura Bradley, "Women with Thick Brows - In Pictures," in AnOther Magazine (August 19, 2011):
The included photo of Ms. Hemingway from a diner scene in Manhattan shows that her left eyebrow is indeed avec (if not on) flick. Ms. Monroee's eyebrows, however, lack any such flick.
And a third mention is in "Fascinating Eyebrow" on All the Tropes Wiki, which uses "eyebrow flick" synonymously with "temporarily arched eyebrow":
So is "eyebrows on fleek" simply a variant of "eyebrows on flick"? Maybe. But even if it is, I can't tell whether being "on flick" originally meant "on point," "well exercised," "well groomed," or something else. To its credit, this second theory ties fleek to a preexisting word instead of conjuring it out of thin air. But the evidence for fleek = flick is far from dispositive.