Applications that run in Adobe Flash Player may want to store some information on your computer, but the amount they can store is limited to 100 kilobytes unless you agree to allocate additional space. Local storage settings let you specify how much disk space, if any, applications from a particular website can use to store information on your computer.
You can read all about Flash's Local Storage here.
To configure it, browse to these webpages (both lead to tabs in the Flash Player's settings manager):
Note, that those settings are global and not bound to the browser. If you change anything with Firefox, the change will also affect Chromium, Opera, etc.