Running the gamut

what does running the gamut mean?

It means the entirety--a sense of completeness.
Someone will use that phrase to describe a state of wholeness as in "The people who frequent the Phrasefinder forum run a geographic gamut with people from almost all continents participating".
Gamut was used by the ancient inhabitants of Rome in a musical sense to desribe a series of notes. I think the original word was "gamus" or "gamuae". I am not 100% on that.