When you admit something, you confess that it happened. It wasn't easy to admit that you'd broken the vase, but how else could you explain that your hand was glued to it?
Besides meaning "confess," admit can also mean "let in," like a theater ticket that says "ADMIT ONE." If you admit that you have a bag of popcorn hidden in your backpack, you might not be admitted to the movie. A doorway admits you into a room, and if a room can hold up to 50 people, that room admits 50. You can even use admit for metaphorical entrances, like the way your wild style admits you into high fashion circles.