I had insurance on myself and my family through an employer that I recently quit working for. What happens to my policy now. Does it just close? Or do I need to do something?

Your HR office should give you info on your COBRA options. You can keep your coverage for up to 18 months in most states. You are responsible for the entire premium and the employer is allowed to charge up to 5% for administrative costs.

You don't specify what type of policy.

COBRA is a US law that requires employers to allow former employees to continue their insurance coverages for up to 18 months. They are requires to pay the full premium but it is the premium charged to the group which should be less than the you would have to pay if you purchase it separately. If you do nothing the policy lapses.