Roleplaying (RP), or Role Playing, in World of Warcraft means taking on the role of a character and acting it out in-game through emotes, /say, /yell, and sometimes other channels. Players may also participate in roleplay outside the game by posting on blogs, wikis, or forums (official or otherwise). Roleplaying has similarities to improvisational theater, with the participants acting out characters in unscripted situations. The character's personality, goals, morals, and quirks may resemble that of the player or be completely different. Regardless, roleplayers recognize a boundary between what is in character and what is out of character.
RP also refers to RP Realms. There are several RP Servers available to Warcraft roleplayers. RP servers are functionally the same as PvE Servers, with added social rules and stricter naming enforcement.
The same is true for RP-PvP Servers and PvP Servers. Both sets of rules apply. RP-PvP is commonly misunderstood to mean that the roleplaying part is optional. In fact, these servers were started in response to petitioning from roleplayers, who felt that the ability to engage in PvP added realism.