When a married couple gets divorced, the state health department or Bureau of Vital Statistics may issue a divorce certificate. This certificate simply states that the individual named is divorced, who they divorced from, and when and where the divorce took place.
There is also an official document called a divorce decree, but it is not the same thing as a divorce certificate. Not all states even issue divorce certificates, and they are not always valid for official purposes. You can, however, usually use a divorce certificate as proof of your divorce or as evidence of a name change when updating your IDs and other documents. If the state where the divorce was finalized offers divorce certificates, you can get one from their vital records office.