"on" - if you get attacked the attacker gets a bounty on his head, in case you are in non anarchy system the police get alerted and based on the sec rating will deploy to your rescue
"off" - attacker does not get any bounty, police do not get alerted - which might be useful if doing some of the hunting missions as you do not have to worry about kill stealing. also if you want to spar with a friend same applies.