So you may or may not have heard about League of Legends (LoL). You may have heard of Heroes of Newarth (HoN) or Defense of the Ancients (DotA), which are similar games. They are all Multiplayer Online Battle Arenas (MOBA). Yeah, acronyms. And yeah, funny names- seriously Online Battle Arena? That is just silly.
Anyways, MOBAs as a genre are mini-rpgs. At the beginning of match [which lasts between twenty minutes and an hour] you select a character and you play as that character for the whole game. There are two bases and lanes between the two bases. Each lane is guarded by towers which are very powerful. Additionally minions or creeps spawn- they are weak NPCs that move towards the other side attacking enemies that get in their way. Eventually, if no players interact one team will randomly win. You take your character and bash things in the face. Overtime, and killing things grants you gold. Helping to kill things and killing them grants you experience. You get more for killing an enemy player or "Champion". You level up, put points in skills (you have four, and they are unique to your champion) and you buy gear that makes you kill stuff faster.
LoL has something on the order of 75+ champions as of this writing and they launch a new one every other week. They have ten free champions and by playing games you earn account bound points (Influence Points) which you can use to buy champions and other things to improve your character. Your account is a "Summoner" which allows you to have masteries (classic talent trees) and you can switch between them before a game to give yourself the advantage. There are also Runes, which give you a straight bonus to a stat, and you unlock more powerful and more stats as you level your account up. Regarding the store, you buy runes and champions with IP (earned in game only) and you can buy new champions and skins for the champions using Riot Points (RP- and paid for with either a game card or online). Since all champions are equal in the hands of equally skilled players, nobody can buy an unfair advantage.
Anyways, on to the game itself. Early game is a lot of harassing- you're unlikely to get a kill on an enemy champion unless they're bad, stupid or you're really good. Later in the game you can just roll over waves of minions easily, but if you're solo-farming you are likely to get ganked by a group of enemy champions.
At low ELO (the rating system) and at lower summoner levels, most players are really casual, especially if you say you're new too. They'll make mistakes, make jokes etc... As you get more advanced the people who talk begin to be more demeaing, yelling, screaming cursing etc... blaming everything on other people and making demands. This was brilliantly demonstrated in this Ctrl-Alt-Del comic. At the same time you'll also find out what kind of champions you like- personally, I prefer carries, specifically melee pushers. Which means nothing to someone outside the game. There are the understandable- support and tanks. And then there are other roles which can get confusing, carries, pushers and junglers. Carries are squishy, but can dole massive amounts of damage, just pouring it on the enemies faces. Pushers can take down a tower solo "pushing" a lane, and improving your teams position on the map. Junglers go into the jungle between lanes killing neutral mobs and then popping into lanes for ganks.
So. I would highly recommend trying the game at least (you can sign-up here for free). If you do find it fun, you can friend me- (US only, sorry) Alenena. If you find yourself interested but want to learn more about a particular character you can use MOBAfire, and look under Builds and Guides (hint- sort by score). Finally, if you end up loving the game, you can apply for one of the many open positions at Riot Games.