1) A hobby in which players create or are given fictional characters to portray. There is usually a rule-system of some form, of which D&D is an example. In a group of players one (or sometimes more) persons will volunteer to be a Games Master - s/he will control all non-player characters, the environment the players interact in and arbitrate the rules.
2) A bedroom practise, in which partners dress up and pretend to be someone else for sexual satisfaction.
"My role-playing character is a barabarian warrior from the tundra!"
"Let's role-play, I want you in that school girl uniform again."