The main purpose of using changing pad covers is to improve the maintenance and cleaning of the changer. In most cases, you should be able to wash your cover in the washing machine with no problem. In any case, it is recommended to pay attention to the manufacturer's instructions before washing it.
Also, take note that many changing pad covers also allow machine drying, without shrinking or deteriorating. Ideally, you want a cover that can be washed with no problems, since we want to make sure it is ready to be quickly used again and again.