These symbols are called Shadowmarks.
Glossary of Shadowmarks (All of the below comes from the in-game book, "Shadowmarks")
"The Guild"
This is the symbol for the Guild. This means the place is as safe as the Flagon's cistern. If you see this shadowmark, someone from the Guild is nearby for certain.
"Safe"
We usually leave this shadowmark when we've scouted and found a safe way around something, a hallway without traps or maybe a house that's already cleared out. If you see one of these, head the way it's pointing and you'll be fine.
"Danger"
If you see this shadowmark, head the other way or take your life in your own hands. It means there's something ahead or beyond that door that wants to turn you inside-out.
"Escape Route"
Now, on the rare occasion (it better be a rare occasion if you want to work in the Guild) that you find yourself in jail, look for this little beauty. You see this shadowmark and escape is just a few steps away.
"Protected"
We put these shadowmarks on places we don't want you to go. As in stay out of there or there's going to be a boot up the backside. These people are under the Guild's protection and should never be robbed or assaulted.
"Fence"
This should quickly become your favorite shadowmark. The person near this mark will buy your... hard-earned stolen goods for a fair price.
"Thieves' Cache"
Who says we only take and never give back? If you find this shadowmark near a chest or maybe a hollowed log, you're in for a surprise... a gift from the Guild for the thief in the field. Whoever said membership didn't have its privileges?
"Loot"
There's something near this shadowmark worth stealing. Saves you from breaking into a place only to find the people don't even have two septim to rub together.
"Empty"
The opposite of the Loot Shadowmark. Pass on this place, there's nothing inside.
You may notice, from time to time, you or enemies will take a few steps back and not act for a few seconds: that's stagger. It's essentially a very short duration stun. Tower of Strength simply reduces the chance of getting staggered by 50%.
Stagger is not affected by Conditioning, which only affects the weight value of equipped heavy armor.
Best Answer
The answer for this question is sort of lacking, so I thought I'd fill in more thoroughly.
The triangle thingy indicates the item, among the various ones you're considering at the moment, that the game thinks is best. "Considering," in this case, refers to the items that are both in your inventory and the inventory of the container or person you're currently interacting with.
Items that you previously owned or that are in your chest at home, etc., are not factored into the game's assessment. The game's assessment is also purely statistical. That is, it picks the "best" item as the item with the highest relevant stat--for weapons, this is the damage stat; for armor, the armor rating.
Even if you're a sneak build, it'll still think the Dwarven Greatsword is the best, and heavy armor is always listed as better than light armor, unless the light armor in question actually has a better armor rating than the heavy armor.
The game does not assign triangles to items that are not weapons or armor. This includes magical amulets and robes--the former because it's actually not a type of armor, and the latter because of its de facto poor armor rating.
There are further subcategories within weapons and armor within which the game will assign triangles--that is, you'll not just have one triangled weapon and one triangled armor. These are, for weapons and armor respectively, bows, one-handed weapons and two-handed weapons and headwear, bodywear, handwear, and footwear.