Roleplaying
Roleplaying (RPing) is acting as if they were the character that he or she plays. Roleplayers create background stories, talk like they were the character and sometimes choose or restrict specific skills that don't immediately benefit them.
A pirate, for example, might pick digging as the first skill and carry abnormal amounts of rum. The pirate would have a background story on how they came to the island, who he or she was and what they were doing there. The character could speak like a pirate and even slur their speech and act as if they were actually drunk.
Sometimes, a serious roleplayer might go out of his or her way to discredit or insult a particular faction, class or action chosen by another player. They might also create causes that seem controversial to what the main population believes and at times going through great lengths to uphold it in ways that he or she believes the character would act.
There are a couple terms used for people that are either roleplaying or not. IC (in character) means the same as roleplaying and OOC (out of character) is acting like themselves.