When you oversleep, you stay asleep longer than you meant to. If you forget to set your alarm clock, you're likely to oversleep.
People oversleep all the time, and they end up being late to school, work, or appointments. No one ever intends to oversleep. If you intend to keep sleeping, you would refer to it as "sleeping in." The verb oversleep is an old one, dating from the fourteenth century, and it's related to the Old English noun oferslæp, "too much sleep."