When you seek a post-judgment modification, you're asking the court to modify the final judgment previously made. For instance, if you have a child custody arrangement in place that doesn't work any longer, you may ask the court to modify that arrangement. If you have a property division settlement agreement that you want to have altered, you can ask for that as well.
You can seek an appeal to ask for a modification of the judge's decision after your divorce is finalized. Usually, settlement agreements cannot be appealed, unless there was a significant problem with how that settlement was reached or there is a problem with enforceability.
An appeal isn't necessarily the best way to have your decree modified, though. A motion to modify your divorce decree may be more appropriate. The motion has to be filed with the same court. You will then need to present evidence of a change in your situation that has created a need for the modification. For example, if you can show that your ex-spouse hid money or that there has been a change in their schedule that requires your custody plan to be altered, then those issues may give you a reason to seek a modification.
A hearing does take place after a modification is requested. If you and your ex-spouse can agree that you want to modify a part of the decree, you may not need to appear at a hearing. That's something that you can both discuss with your attorneys if you find that you want to make a change to your divorce decree.