A stethoscope was a medical device used by physicians to listen to the sounds made by a patient's heart and lungs.
In 2151, the surgeons at Starfleet Medical, including Dr. Phlox, wore stethoscopes while treating the Klingon Klaang. (ENT: "Broken Bow")
Q wore a stethoscope when he appeared to Captain Jean-Luc Picard dressed as a doctor in 2369. (TNG: "Tapestry")