"The normal mod. representation of OE. græf would be graff; the ME. disyllable grave, from which the standard mod. form descends, was prob. due to the especially frequent occurrence of the word in the dat. (locative) case. [OED]
From Middle Ages to 17c., they were temporary, crudely marked repositories from which the bones were removed to ossuaries after some years and the grave used for a fresh burial. "Perpetual graves" became common from c.1650. To make (someone) turn in his grave "behave in some way that would have offended the dead person" is first recorded 1888.