At its most basic level, it simply means staying in character, saying what your character would say and doing what he/she would do, rather than talking about the game as being a game or about unrelated real-life topics.
Some people go beyond that basic into developing extensive histories of their characters, and how they came to be where they are. (Ironically, this ends up leading some of them to abandoning the basic "staying-in-character" aspect of roleplaying, so that they can tell their stories to each other instead. There's a fair amount of overlap between roleplayers and storytellers, though, so sometimes the two playstyles are lumped together and both referred to as RP.)
