A force field generator was a piece of equipment that was used to project a force field over a specific area.
On the Gorn controlled world of Seudath, the Klingon Imperial Intelligence agent Goloth destroyed a force field generator with his disruptor pistol in an attempt to flee from two Starfleet Intelligence agents. (VAN - Declassified novella: The Stars Look Down)
In the 23rd century, Kalins on the Balant planet were able to harness electrical energy generated by native trees to power a force field generator. It was used to defend their settlement from meteor bombardment and attacks by Balants. (TOS comic: "Skin Deep")