Hiya!
I'm not sure what in particular you are asking about, so I'll offer a couple of responses:
1) If you crash or leave the game while in combat, the server keeps your character on to fight until the battle is finished one way or another. This is to prevent players from logging out in the middle of a fight without any consequences.
2) When you go offline normally, your character too "disappears." Many people roleplay this as having their character go do his/her own thing, like traveling, resting, etc. But your character is not logged on in any form if you aren't.