Out-of-character boards at Pro and MB are places where members post as themselves - that is, not as narrators telling a story.
[General Chat] is an entirely OOC board. Storyboards all have an OOC section for the writers to discuss things related to the plot and what's happening next.
Any board that does not form part of a character/setting's 'official' or 'canonical' story is out of continuity.
The Cross'd Roads inns and party boards are considered "out of continuity unless we don't want them to be". Writers can decide together to make something that happened in Cross'd Roads part of official continuity.
IC means 'in character'. Some boards or writing may be written in-character but not be part of an official storyline (i.e. they are out of continuity). These include Character Chat and the blogs kept by some characters. In-character, out-of-continuity boards are primarily used to develop the character and fill in backstory.
The acronym OOC can also be used in the sense of behaving out of character (doing uncharacteristic things).
It's generally a criticism in this sense when applied to writing, although it may be a good thing if it means people have picked up on a deliberate clue that all's not right with the character.