MMORPGs have characters that you create and advance in level, gear, powers, etc.
I'm not sure how other MRTSs work, but League of Legends doesn't have a character you create. Instead, what you have is a summoner which is basically the word they use for the player controlling the champion. A champion is a set character in the game with set abilities. The only times those abilities change are if the champion levels up during a match (or if developers decide to tweak them with patches). Every match begins each champion at level 1, and through killing NPCs and enemy champions, you earn experience for your champion in that match.
After the match is over, a game overview screen will tell you the stats of the game (how many champion kills each summoner had, how many deaths, and how many assists in killing enemy champions). It will also tell you how much experience the summoner received for that match. Winning a match gives more experience than losing a match, but a each summoner receives experience regardless of the outcome (unless they're already at maximum level).
So really, instead of advancing a character as in an MMORPG, you're advancing your summoner (which is a fancy word meaning your account), and leveling up your summoner allows you to open more rune slots (which increase champion stats during matches) and access to more summoner spells (spells that anyone, regardless of the champion they are playing at the time has access to).
With this set up, you can tailor your summoner account to boost certain stats in game, and depending on which champion you choose to play will really determine what stats you want to boost.
Shjade pretty much covered the in-game part describing the equipment and such.