(covers information from several alternate timelines)
A mek'leth was a traditional Klingon bladed weapon. While Klingons often carried disruptors, they prefered to use bladed weapons in combat, with the two most common ones being the mek'leth and the bat'leth. (ENT: "Marauders")
Captain Gabriel Lorca owned several Klingon blades, including a mek'leth. Ellen Landry wanted to use it to cut off the claws of "Ripper", but she was killed by the creature. (DIS: "The Butcher's Knife Cares Not for the Lamb's Cry")
Jadzia Dax thought that, although the mek'leth was better in some ways, she still preferred the longer reach of the bat'leth. She later practiced with a mek'leth. (DS9: "Sons of Mogh", "Rules of Engagement", "Bar Association")
During the Battle of the Binary Stars, T'Kuvma used a mek'leth to battle Captain Philippa Georgiou aboard the starship Sarcophagus in 2256, eventually stabbing her to death with it. (DIS: "Battle at the Binary Stars")
When Michael Burnham challenged Kol to a duel in order to buy time for the USS Discovery to complete its readings of the Sarcophagus cloaking device, he tossed her a mek'leth. (DIS: "Into the Forest I Go")
Worf occasionally favored the smaller (and easily concealable) mek'leth instead of the larger, bulkier bat'leth. (DS9: "The Way of the Warrior") Worf often used his mek'leth to fight the Jem'Hadar, such as those on Vandros IV and on Soukara. (DS9: "To the Death", "Change of Heart") He also concealed his mek'leth on his EV suit during a spacewalk on the hull of the USS Enterprise-E, tucked into the suit's belt at the small of his back while in orbit around mid-21st century Earth. He used it to kill one of several Borg drones that had been building an interplexing beacon on the ship's deflector dish. (Star Trek: First Contact) In an alternate timeline on Gaia, Worf's descendant Brota inherited his mek'leth. In this timeline, he had once used it to kill a yar-bear. (DS9: "Children of Time")
The mirror universe Bareil Antos claimed that he had once stolen a mek'leth from his Klingon guard and had then used it to deactivate the sensor alarm of a cell in which he had been held. (DS9: "Resurrection")
One of the Klingon holograms in a simulation used by the Hirogen wore a mek'leth while singing Klingon drinking songs at a campfire. Later, some Klingon holograms used their mek'leth's to attack the Nazi holograms. (VOY: "The Killing Game", "The Killing Game, Part II")
Dan Curry created the mek'leth at Michael Dorn's request when he joined Deep Space Nine in 1995. Dorn wanted a weapon that was easier to wield. The final design was based on a Himalayan blade, a Northern Tibetan cavalry sword. However, the ergonomics of the weapon were specifically designed for Dorn's mass and hand size. (Star Trek: Deep Space Nine Companion; A Vision of the Future - Star Trek: Voyager) This original sword inspiration appears to be the Nepalese kora.
The mek'leth from Star Trek: Discovery was created in Toronto, Canada. It was made from hand sculpted high-density foam. That sculpt was subsequently converted into a 3D model and milled out of aluminum. The blade's elaborately detailed surface was hand carved from a poured resin. The weapon's handle was also hand carved from foam and then cast in resin. ("Star Trek Exhibition" at DIS: "Si Vis Pacem, Para Bellum" screening, Millbank Tower, London, UK, 5 November 2017) One of these mek'leth props was featured at Star Trek: The Exhibition in Blackpool, UK, and is now on a world tour.