A bird such as a hen that sits on eggs to incubate them can be said to hatch the eggs. Then, when the chick emerges from the egg, you can also say it hatched.
Humans don't hatch eggs like birds do, but they can still incubate and then hatch a plan, invention, or idea. You may hatch a plan to surprise a friend for her thirtieth birthday party, but to ensure you don't end up with egg on your face, you should verify your friend isn't actually twenty-nine for the third year in a row! As a noun, a hatch is a trapdoor or other opening in the floor, ceiling, or wall that allows access.