The Grandfather paradox is a paradoxical situation arising in time travel. Supposing a time traveler went back in time and killed his grandfather before siring the traveler's father - the traveled would never exist to travel back in time in the first place and could never have killed his grandfather. The term is more generally applied to any situation or action which would logically make impossible the ability to travel backwards through time in the first place.
When Montgomery Scott went back in time to attempt to save James T. Kirk before he could be absorbed into the Nexus, he was concerned about the timing of transporting Kirk off the USS Enterprise-B; too early, and the Enterprise would not be able to break away from the energy ribbon, and the Scott of the time would be killed, and logically unable to travel back in time. (Star Trek novel: Engines of Destiny)