Departments look at their yield and decide whether to go to their wait list.
(1) If you are a waitlist that you prefer to your best current offer, accept the offer you have by the deadline.
(2) If you are on the waitlist for a place you would definitely go to, tell them. Even if you have already told them, tell 'em again. (No fibbing though--people have long memories.)
(3) A fairly small number of offers do go out after April 15, usually quite soon after April 15, as departments find they didn't get as many acceptances as they wanted by the deadline or that someone who has accepted has then withdrawn their acceptance.
(3) If you get a preferred offer after April 15 and you have already accepted another offer you need to inform the department where you had accepted that you are withdrawing. Do so VERY politely. But it is okay to do.