For the most part, apps just stop updating. There are some internet connected apps that will stop working (e.g. banking and finance) but most apps will continue working - you'll just be using an older version.
I've still got my iPad 4 128GB on iOS 6. I'm loathe to update as that combination has a level of smoothness that still hasn't been matched by any iPad running iOS 7 or higher. I guess too much eye candy. I mostly use the iPad 4 for DRM free comics and manga (via ComicGlass) and occasional web surfing. Interestingly enough, I believe ComicGlass is still getting app updates for iOS 6. It actually takes developers a while before dropping continued support for old iOS versions.