Nothing really happens on the Adobe Flash side, other than an insecure piece of software can finally be removed from your pc!
Modern browsers already have the goods in them to do everything the old Adobe Flash piece did, so just keep your browser updated, and you're in business!
Note that you might have some other old program that also depended on the old Adobe Flash technology ... if so, just get that old program updated as well, or find out how the program's author wants you to handle the issue.
An old post, but now it has the technical answer, if anyone else searches on it ...