(covers information from several alternate timelines)
A comet was a celestial body, usually orbiting a star, composed of rock and ice. If a comet approaches close enough to a star, the increased heat causes it to shed mass away from the star, creating a coma and/or "tail".
In 2151, the Earth starship Enterprise NX-01 discovered the largest comet yet observed by Humans or Vulcans, with a diameter of 82.6 kilometers. It was named Archer's Comet for Enterprise's captain, Jonathan Archer. (ENT: "Breaking the Ice")
In the 22nd century, many comets in the Sol system were diverted to Mars by the verteron array for the Martian terraforming project. At one point, fourteen comets were scheduled to impact with Mars in a thirty-month span, starting with the arrival of comet Burke in January 2155. (ENT: "Terra Prime")
The USS Enterprise-D tracked a rogue comet through Sector 1156 in 2370. Its core, composed largely of fortanium, proved to be a D'Arsay cultural archive, built over eighty-seven million years previous. (TNG: "Masks")
While under the influence of Saltah'na energy spheres, Commander Benjamin Sisko compared his name with a comet who would blaze across the stars long after Kira's petty treacheries would be forgotten. (DS9: "Dramatis Personae")
In 2371, the wormhole relay station experiment, conducted by the USS Defiant in the Gamma Quadrant, diverted a comet laden with silithium towards the Bajoran wormhole. Some interpreted this comet as the "Sword of Stars", an element in Trakor's Third Prophecy. (DS9: "Destiny")
When Chakotay tried to erase a comet which had forced the USS Voyager to enter Krenim territory several months beforehand, he altered the timeline by wiping out almost 8,000 civilizations, as life within fifty-thousand kilometers around the comet would have never existed. Four billion years ago, hydrocarbon fragments of this comet erased plant life on a planet. (VOY: "Year of Hell, Part II")