RPG stands for "Role Playing Game," and refers to any of several types of interacive games in which the player assumes the role of a character in the game. There are two main types of RPGs: Videogames and Table-top.
RPG Videogames follow a set story, and are usually layed out in a similar fashion. Your character and comrades that you meet along the way fight badguys and monsters together, meet people, help people, uncover plots, and usually end up having to save the world. The scope of most Videogame RPGs is almost comically large. Battles are usually fought in a very unrealistic, menu-based manner, in which a certain number of your comrades (usually three) takes on a certain number of enemies. These battles normally happen at random intervals while traversing hostile territory. Personal statistics, like attack power, defense, and life, are displayed as numerical values on the screen. Once all of the enemies are defeated, the battle ends. An RPG videogame is like a novel: its replay value is based mostly on the player's desire to wittness the story unfold again.
Tabletop RPGs are much different. They are played by a group of people who take on different identities for the game. There is usually one person, the Game Master (or similar title) that creates a story and provides the narration. Battles are fought using rolls of dice, or other means, which represent unique attacks and abilities created by the players. Characters in tabletop RPGs have stats as well, and just like in VG RPGs, their attributes increase numerically with their conquests.