Camo is a status which prevents other people from attacking you for a period of time. You lose the Camo when the time runs out, or when you attack another island.
When your base is destroyed by an enemy attack, you automatically get Camo for at least an hour. You can also purchase longer-lasting Camo from the Treasury.
If you have any further questions about this or Battle Islands in general, please go to this page and fill out the game questionnaire!