RPG or Role Playing game is a type of game where you use your character in a certain way (fight, train, study something, etc.) and build in levels to become stronger in strength, intelligence, skill, health and/or magic power. Also, RPG's are known to have great story line and take months to beat. 

There are many different game that are RPG's: Final Fantasy (numbered and unnumbered. ), Dark Cloud, Pokemon, Shenmue (my favorite by the way.), etc.