Getting a final judgment of divorce means that you are no longer legally married. It doesn't necessarily mean that you and your spouse no longer have any legal obligations to each other--if your marital settlement agreement or judgment says that one of you must pay support to the other, or that you're going to continue owning property together for a certain period of time, then you must comply with those terms. And of course, if you have children you will continue to coparent according to the terms of your settlement or judgment. In all other respects, you're free to do as you please, including remarrying.
However, there are quite a few details that you will need to take care of after your divorce is final. It's really important to handle these post-divorce tasks, so that you don't end up in some kind of fix because you didn't change your marital status or a beneficiary designation on some important paperwork. Here are some articles about the things you need to be sure to do once your divorce is completed.