You hatch eggs, pick a fighter, and send it into the PIT to earn money. Corn and Cash go back into that bird, the coop, and the next hatch. Climb the TOWER when the same chicken can beat bosses. Those floors are also the gate for Rebirth.
Named chickens lay named eggs, so a layer that opens your next hatch pool is worth more than a rare that does not. Fusion spends a donor to mutate the base, and a Special only sticks if the live FUSE preview locks it. Rebirth resets Cash, level, and coop, keeps the flock, and pays you faster the next time around. Eggs keep dropping while you are offline.