If you are quick, you move with speed. You may be a quick runner or "a quick study" — if you tend to learn things quickly.
The adjective quick can also mean brief and fleeting — as in a quick visit or a quick trip to the store. Quick also means without delay: "You'll need to jot a quick reply to the party invitation." The noun quick is a whole other story; it's a highly sensitive bit of skin, especially the skin under the fingernails or toe nails. Be careful not to chew your nails down to the quick — especially your toe nails.