Outlaws are those Characters who have a less than -50 Citizenship Points. Between -50 and -250 CP you remain as an Outlaw.
This sign will appear above an outlaw character's head when they cross -50 Citizenship Points threshold.
An Outlaw can become legal by performing actions which increase their Citizenship Points until the total value is positive again, or they can go to jail (whether voluntarily or after being killed by another character).
Any action with the red olive branches icon on it will give you more negative CP.
Other players can attack you and try to send you to Jail by defeating you in combat while you are an outlaw. This action (if succeeded) will provide them Citizenship Points and help them unlock Guard status. So stay low while you are tempering with your nation's law if you want to avoid player versus player combat.