A breathing apparatus was a piece of equipment that allowed an individual to breathe their own form of air while in an alien atmosphere.
Jadzia Dax recalled the story of a hydrogen-breathing Lothra and an Oxygene who fell in love and yet could only be in the same room for forty minutes a day without their breathing apparatus, nonetheless staying together for fifty-seven years. She gave Melora Pazlar this example to convince her that a relationship with Julian Bashir wouldn't be impossible, despite the differences between them. (DS9: "Melora")
Barzans had to wear breathing devices when leaving their homeworld Barzan II. The device provided them with the gasses that were found in the atmosphere of their homeworld that were toxic to other species. (TNG: "The Price"; DIS: "Project Daedalus")
Some Benzites were unable to breathe a standard oxygen/nitrogen atmosphere, and therefore had to wear a breathing apparatus in those environments during the early 2360s. By the early 2370s, this device had largely fallen into disuse, though at least one Benzite serving in Starfleet still employed a breathing apparatus in 2380. (TNG: "Coming of Age"; DS9: "The Ship"; LD: "Second Contact", "Moist Vessel")
