A particle accelerator was a device that propelled particles to high speeds. It could be used as a weapon.
In 2370, Quark arranged to have the Maquis gunrunner Sakonna acquire three particle accelerators from the Pygorians. (DS9: "The Maquis, Part II")
The crew of the Silver Blood USS Voyager acquired some particle accelerators in 2375. (VOY: "Course: Oblivion")
According to Star Trek: The Next Generation Technical Manual, (p. 123) for Starfleet, the invention of phasers replaced the application of particle beam accelerators and lasers as starship weaponry.