PASUI is a mandatory unemployment tax that is paid to the state. There are 2 parts, the employee portion that is is usually a very small amount - around .0006 times your gross pay; and the employee's portion - about 30 times your portion. I believe it just goes to help pay everyone's unemployment costs, much like social security: you're not using it right now, but your deduction helps to pay social security for those now collecting it.
