A coffin is an oblong box, usually made of wood, in which a corpse is buried.
In 2154, the coffins of the Human casualties of the United Earth Embassy bombing on Vulcan were lined up in the cargo bay of Enterprise NX-01, draped in the United Earth flag, ready for transit back to Earth. (ENT: "The Forge")
In Starfleet, in the 22nd and 23rd centuries, it had become something of a tradition to place the bodies of dead crewmates in the empty casing of a torpedo, much like a coffin, before launching them out into space. (ENT: "Similitude"; Star Trek II: The Wrath of Khan, DS9: "The Sound of Her Voice", VOY: "Latent Image", "One Small Step" et al)
In 2365, Emissary K'Ehleyr referred to a modified class 8 probe as a coffin after she endured a trip at warp 9 in it, in order to rendezvous with the USS Enterprise-D for an important mission. (TNG: "The Emissary")
In 2370, Doctor Beverly Crusher read an eulogy before her late grandmother's coffin on Caldos II, with Counselor Deanna Troi and Captain Jean-Luc Picard by her side. The coffin was later beamed back from the underground to scan Felisa Howard's dead body for anaphasic energy. (TNG: "Sub Rosa")