"Metroidvania" is a term used to describe a sort of exploratory 2D platforming game. It comes from the original games of the Metroid series and some of the middle-era of Castlevania games (most notably "Symphony of the Night", which is what primarily gave birth to the term).
The most defining feature is usually the world. Rather than have set stages or a world map, the entire game takes place inside one giant map, which you must traverse about. Not just any map, but typically a very complex map filled with all kinds of secrets. The map is typically divided into sectors, more in an aesthetic fashion to denote that the denizens and dangers will be different. Sometimes you have teleports to assist you in travel, but other times you just have to remember where to go in the map.
There's various elements at play in the exploration. There's typically tidbits hidden in spots, or puzzles that have to be returned to when you find appropriate equipment. The exploration is also non-linear - your limits of progression through the map are by various tools or powerups that you need to acquire, but the order in which you must acquire some of these tools is not set. And in many choices, there are many paths to get those tools, or even get past obstacles without those tools.
A very popular element of these games, especially in the Metroid franchise, is the concept of "sequence breaking". Using special tricks or otherwise mastering the utility of your basic abilities, you can sometimes access items and areas far earlier than the game expects you to.
As far as I know, Metroidvania games have always been 2D platforming games. Aside from the elements of exploration, the actual gameplay of Metroidvania games vary widely.
There is not a clear definition of MOBA out there, so let's define it.
MOBA is a genre definition for multi-player games where not only two parties struggle for resources or attack/defend, but each party/person is against all others in a confined space, therefore the term arena.
Battle arenas in real terms had a pre-defined resource collection: Multiple entry points for opponents, and spread out in the arena, weapons and shields.
Loosely defined, one can see it as a mixture of RTS/RPG and Free-for-all deathmatch, the emphasis is in some games on the former part (DoTA-type games) and in others on the latter (Monday Night Combat).
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When commentators of a fighting games are talking about + or - on block they're specifically talking about frames. To understand this concept, you have to come to terms that fighting games operate at a predefined rate. The rate of which a fighting game operates is often declared in frames per second (fps), literally how many frames or timesteps occur per second. Most fighting games today operate at 60fps so in other words within each second you can split the game into 60 separate states.
Coming back to frames it's best to explain it with an example. So in Tekken most jabs offer +1 frame advantage on block. This means that if the attacker's jab is blocked the opponent CANNOT perform any action in the next frame. That is, the defender cannot do anything for the next 1/60th of a second. So if both players are mashing jab after the initial jab is blocked, the defending player will always lose because he is in a -1 frame disadvantage or his jab will come out 1/60th of a second after the attacker (who has a +1 frame advantage).
Conversely in a -frame situation, for example getting an uppercut blocked in Street Fighter. The attacker cannot perform any action while recovering from the move, hence he is both in a frame disadvantage and punishable. So it can be stated that if a player is in -n frame disadvantage, he is punishable by moves which can connect in <=|n| frames.
This is of course just the tip of the iceberg when discussing frames, one could go into details regarding frame traps and other intricacies. You can get more information regarding frames from dedicated fight game forums, I highly recommend UltraChenTV's episode on frames