Cooldown is where the Police cannot see you but you are still in a Pursuit. So you can still be caught. If the police see you, it resets the evade/busted bar and you have to do it again. Your cool down time if affected by your Heat Level and if you go into special cool down areas.
When you are in one, your cool down bar will go up faster, allowing you to evade the pursuit quicker. When you are in one, the police cannot see you, but if you crash into them, it will start the pursuit again. When you are in cooldown mode, you can enter the Safehouse to end the pursuit.