RP, or roleplaying, is the act of portraying your character as who you are, rather than recognizing that it's just an imaginary person you are controlling with a keyboard and mouse. The opposite of roleplaying is meta-gaming.
Someone who is roleplaying will take lore very seriously as a whole, and try to understand the world around them. They will also create a backstory for their character as to what they did earlier in life and why. Often, this forces them to behave in certain ways that a "normal"-server player would not do.
Roleplayers also communicate with each other in appropriate ways. L33tspeak and internet slang are omitted from their vocabulary, and references to the outside world are usually not referred to, or spoken of in limited circumstances, perhaps with the notation "OOC" for out-of-character.
In short, role-players are actors.
Role-playing is not a style of play that most players involve themselves in. It can be slow and tedious to someone who is objective-minded and wishing only to get to the next level or acquire new loot. Because role-players are a secluded bunch with very different interests, there are special servers that are intended specifically for role-players. If you create a character on one of these servers, please keep their purpose in mind. The other players will not look kindly on someone who constantly shouts out nonsense about the latest sporting event or refers to a website when someone asks for help.
American RP servers include: