Factor of gravity. It is used to express the apparent increase of mass due to inertia. While the actual mass of an object remains the same, during manouvering this object is apparently heavier. The G factor quantifies how much heavier.
A mass of a pilot is 80 kg. When manouvering at 3G, the pilot mass is still 80 kg, but the apparent mass that the seat has to carry is 3 (G) X 80 kg = 240 kg.