A painkiller is a medicine that eases one's pain.
Doctor Beverly Crusher gave Jean-Luc Picard a painkiller when he was experiencing an unknown form of pain when DaiMon Bok returned his previous command starship, the USS Stargazer. (TNG: "The Battle")
In 2372, Doctor Julian Bashir gave Norva a painkiller. However, it had no effect as she was experiencing the final stages of the Teplan blight. (DS9: "The Quickening")
After Jadzia Dax was injured by a Jem'Hadar weapon on Soukara, Worf gave her painkillers, although the anticoagulant from the Dominion weapon meant she needed to take more. (DS9: "Change of Heart")