A generator was a means of producing generating power on planets, starships, and other fixed installations, such as starbases. It provided power for shields, phasers, replicators, and other on-board devices.
When Major Kira Nerys tried to confiscate a shipment of dolamide from a Valerian transport in 2369 for proof they wanted to ship it to the Cardassians for their weapons, Commander Benjamin Sisko refused. According to Sisko, dolamide was also used for power generators, reactors, and in short-range transports. (DS9: "Dramatis Personae")