Feats are special objectives that you work on over a longer period. For instance, some feats might challenge you to log in daily for a certain number of days. Once you hit that target, the feat can continue to the next milestone (like 7 days, 30 days, or even 100 days). It's an enjoyable way to get extra rewards just by enjoying all the game has to offer!
Feats are located in your Player Profile tab that you can easily reach by tapping your Player picture or name on top of the main Flock screen.