Ovoviviparity is a reproductive system in which a female animal produces eggs which are internally fertilized but are kept inside the mother's body until they hatch, at which point the babies are released.
To a casual observer this would look a lot like viviparity, which is how mammals produce their young. However there are some important anatomical and evolutionary differences. In viviparity the developing young are typically encased in a placenta, and are getting nourishment from the mother's body. In ovovivparity, the offspring are nourished by a yolk sac which is not connected to the mother. However in both viviparity and ovoviviparity, oxygen and carbon dioxide are exchanged between the offspring and the mother's body by diffusion.
Most shark species are ovovivparous, as are some bony fish such as guppies. A couple of really unusual examples would be the gastric brooding frog Rheobatrachus silus, an Australian species in which the female swallows her fertilized eggs and holds them in her stomach for more than a month until the hatch, and seahorses, in which the female transfers her eggs into a special brooding pouch on the male's belly, where they remain until they hatch.