From what I understand of this process, the big May 15 date is the day for anyone with multiple acceptances to withdraw from all but one.
This frees up those spots for the people on the waitlist to move into the class. Since many of the waitlists are unranked, etc., it takes time for the schools to determine who they ultimately want to give that seat. The schools might still be interviewing to fill those seats. (This might be the time to again express interest in the schools where you're on a waiting list.)
If a student already decides upon 1 school between his myriads of acceptances (the lucky bastard) on May 15, but is still on the waiting list for a school he ranks higher, he can decline the acceptance he chose for May 15 and go with his higher choice. (Of course in this scenario, any male pronoun could be replaced by a female pronoun.)
I hope that clarifies some stuff.