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The Grandfather Paradox is a paradox of time travel. The paradox is as follows: "Suppose a man traveled back in time and killed his biological grandfather before the latter met the traveler's grandmother. As a result, one of the traveler's parents (and by extension, the traveler himself) would never have been conceived."
When Colonel Cameron Mitchell, Colonel Samantha Carter, and Dr. Daniel Jackson were sent to an alternate timeline through the Stargate due to Ba'al's actions it was found out that Ba'al had killed Mitchell's grandfather aboard the Achilles causing both Dr. Bill Lee and Carter to comment on the fact that Mitchell was a literal Grandfather Paradox. (SG1: "Continuum")
The paradox is derived from attempting to combine time travel with the laws of classical physics. However, when one combines time travel with the laws of quantum physics, the paradox is resolved: the time traveler is sent to a parallel universe.