As stated by Microsoft:

The Program Compatibility Assistant detects known compatibility issues in older programs. After you have run an older program in this version of Windows, it notifies you if there is a problem and offers to fix it the next time you run the program. If the compatibility issue is serious, the Program Compatibility Assistant might warn you or block the program from running. If that happens, you’ll have the option to check online for possible solutions.

For example, the Program Compatibility Assistant can resolve conflicts with User Account Control, a new security feature in this version of Windows that can help make your computer safer. Or, it can run the program in a mode that simulates earlier versions of Windows. The changes that Program Compatibility Assistant makes are done automatically, so you don’t need to make them.

Here’s more detailed information as well. If you know all your applications are compatible, or you don’t care to get any assistance in making them compatible, you can safely disable this service.