A Key Distribution Center (KDC) is a system used for securely exchanging secret keys. It makes sure that only the people who are supposed to have the secret keys actually have them.
Think of it like a locked box. Inside this box is a special key - the secret key. The people who need to have the secret key come to the locked box and the KDC unlocks it. The KDC then gives the people the secret key, making sure that only the people who are allowed to have it can get it.