Quake II is a first person shooter developed by id Software and released for PC in November 1997. It is not a sequel to Quake, it just shares the name of the franchise;
The old story was that Quake II which has nothing to do with Quake I was going to be a completely different name, but we got fed up with getting the names rejected so we said, "Dammit, it's Quake II. We own that trademark."
John Carmack interview at QuakeCon 2007