Adding to what Purdue said, the first 15 or so degrees of flaps add mainly lift while progressing beyond 15 or so adds more and more drag w.r.t. (with respect to) lift.
Also, there are different types of flaps:
Plain - simple hinged devices that move in a way similar to the elevators
Fowler - complicated devices that rotate down and slide aft. In the initial stages of extension, they mainly slide aft, adding to wing area and lift, further along in the extension progression they rotate down more and more.
Slotted - similar to plain flaps except there is an open slot between the flap and the wing when extended. This allows air to sneak through and holds the airflow more tightly to the wing. NOTE: Cessna high wing flaps are sometimes referred to as "slotted Fowler flaps" because they have similarities to both types
Split - surfaces that rotate down from the underside of the trailing edge of the wing.