1. An abbreviation of "I see".
2. An abbreviation of "In Character" which refers to roleplays and RPGs. This means that what you are saying is in the voice of your character, in contrast to ORP or OOC which means you speaking as yourself, not your character.
1. Lola: I was so pissed this morning when Jenna said she couldn't drive me anymore, which is why I was so rude to you.
Amanda: Ohhhh IC!
2. ORP: My internet was off, so I couldn't reply! SO sorry!
IC:
He never looked back as he walked away from Artie and all of his dreams.