To become baby birds, eggs must be warmed to around 98.6 °F and remain at that temperature while the embryos develop. Adult birds that incubate(*) have special equipment to accomplish this: bare skin on the belly called a brood patch.
We don't usually see the brood patch because surrounding feathers close over it to keep the adult warm. When a bird comes back to its nest to incubate, it opens its belly feathers to lay its bare skin against the eggs. You may have seen peregrines open their belly feathers by standing over the eggs and rocking side to side.
Click on the link below to see an American kestrel's brood patch and learn about this important part of bird anatomy, the Brood Patch.
(*) p.s. In eagles and peregrines, both sexes incubate so both have brood patches but this isn't the case with all birds. In many duck species, only the female incubates so the males don't have brood patches.
(photo from the National Aviary falconcam at Gulf Tower)