Question: What is the Hatch?
The term "hatch" was first introduced in (Ep: 1x13, Hearts and Minds).
Answer: While looking for Claire, who'd been abducted by Ethan, Locke and Boone find something metal in the ground (Ep: 1x11, All the Best Cowboys Have Daddy Issues). Without telling anyone else about it, the two dig it out to find it is a hatch that leads down into a big building.
Locke tries several times to get into the hatch, but only succeeds after going to the Black Rock for dynamite. (Ep: 1x23, Exodus Part 1)
Inside the hatch are living quarters, complete with a bedroom, kitchen, armory, food closet, and a button that needs to be pressed every 108 minutes.
They also find a man down there, Desmond, but he runs away. Locke takes over Desmond's job of pushing the button every 108 minutes, until he decides the button shouldn't be pushed. When the button is not pushed, Desmond turns the failsafe key and the hatch implodes (Ep: 2x23, Live Together, Die Alone).
