In roleplaying games, In Character (or IC) refers to the world of the characters, rather than the world of the players. That is, a character talking to another character is an IC interaction, set within the IC world, while two players talking about a football game or their real lives is an Out of Character (OOC) interaction.
Most online role-playing communities make allowances for the intrusion of "RL" (real life) by introducing standards of communication, such as insisting that all "OOC" comments are placed inside brackets, or given some prefix. For example, "(OOC) Blast, the phone's ringing again, I'll go and pull it out of the wall."
In addition to this very clear distinction between real world and fictional world, IC and OOC are used to refer to more subtle distinctions as well. Dedicated roleplayers are known for pouring themselves into their characters much as actors might. In this subtler context, a character's action, while prima facie valid (i.e. not flatly contradicting the setting) might seem to poorly portray a character. Thus, IC and OOC are basic concepts for roleplaying, and complaints/praises about player behaviour will often employ them. For example, "That was funny, but not really in character." (This would suggest that the action in question was not something the character would have likely done; rather, the player of that character is being criticized for trying to get laughs by breaching realism.)