A baryon is a subatomic particle, a hadron (a group of elementary particles that experience strong nuclear force) with a non-integer spin. Baryons accumulated aboard starships as a result of warp travel. They could be removed at facilities that performed baryon sweeps, a procedure lethal to organic material.
Captain Jean-Luc Picard was trapped aboard the USS Enterprise-D during a baryon sweep at the Remmler Array in 2369. (TNG: "Starship Mine")
When Quinn transported the USS Voyager to just before the Big Bang in 2372, a build-up of baryonic particles was detected outside. (VOY: "Death Wish")