(covers information from several alternate timelines)
|Location:||In orbit of Qo'noS|
Praxis was the inhabited sole natural moon of Qo'noS. It was used as the Klingon Empire's key energy-production facility in the 23rd century. (Star Trek VI: The Undiscovered Country; VOY: "Flashback"; TNG: "Sins of the Father"; Star Trek Into Darkness, display graphic)
In 2293, Praxis was destroyed in a large explosion caused by over-mining and insufficient safety precautions. The explosion caused a powerful subspace shock wave that impacted on the USS Excelsior, a Federation starship outside the Neutral Zone heading back to Federation space under full impulse power after a three year assignment in the Beta Quadrant.
Praxis' decimation resulted in a deadly pollution of Qo'noS' ozone, threatening the depletion of their oxygen within approximately fifty Earth years. Due to the Empire's enormous military budget, their economy did not have the resources with which to combat the catastrophe, forcing Chancellor Gorkon to approach the Federation with an overture of peace. This set into motion a series of events, eventually resulting in a lasting peace between the Federation and the Empire. (Star Trek VI: The Undiscovered Country; VOY: "Alliances", "Flashback")
The explosion of Praxis is loosely based on the Chernobyl disaster, one of several factors leading to the breakdown of the Soviet Union. (Captains' Logs: The Unauthorized Complete Trek Voyages, pp. 137-138) Likewise, the word "Praxis" is employed in the writings of Karl Marx, meaning active rather than merely theoretical socialism.
Praxis' destruction in Star Trek VI (particularly its placement at the start of the film) was influenced by a clap of thunder that begins Macbeth. In the playwright workshop at the University of Iowa, Nicholas Meyer (who co-wrote the screenplay of Star Trek VI and directed the film) learned was a very effective method of attracting an audience's attention to the story. (audio commentary, Star Trek VI: The Undiscovered Country (Special Edition) DVD)
In a scripted line not included in the actual film, Praxis was to have been established as having no indigenous lifeforms.
According to the Star Trek: Star Charts, on page 61, Praxis was located in a separate system from Qo'noS. This system was closer to the Federation-Klingon border. In this system, Praxis was located in the Praxis system. System's primary was a Class M star. The system was located in the Beta Quadrant.
In Star Trek Into Darkness, the Enterprise journeys to Qo'noS, and a large moon fragment strongly resembling the remains of Praxis can be seen. Co-writer Alex Kurtzman stated "It certainly was inspired by Praxis, however, it's not specified, so we're leaving it open as to exactly what that moon was."  Roberto Orci agreed in a comment on Twitter, stating that the moon was "not specified as Paraxis [sic]. But could be" 
A planetary codex for Qo'noS seen in the film identified Praxis as the moon of Qo'nos, and listed it as destroyed. 
According to the novelization of Star Trek Into Darkness the broken moon orbiting Qo'noS was Praxis.
In the Star Trek: Myriad Universes story The Chimes at Midnight, set in an alternate timeline (specifically, the one from TAS: "Yesteryear" in which Spock died as a child), Praxis is chosen by Thelin in 2290 as the test site for the Genesis Device (which in this timeline had led to full-scale war) both as a demonstration of force and because, with nearly all of its inhabitants living in areas either underground or shielded, there would be little or no loss of life. The action forces the Klingon surrender – unfortunately, the Genesis Wave overwhelms most shields and reaches below the ground, and of the population of half a million, only 2,000 survive. However, during peace negotiations, it is discovered that Genesis actually saved the moon, as the explosion which occurred in the prime universe had been inevitable within a year before the wave had strengthened the planet and put an end to the mining that would eventually destroy it.
In the novel Sarek by A.C. Crispin, in addition to polluting Qo'noS's atmosphere, Praxis's explosion has created a ring of debris around the planet that subjects the surface to constant, and sometimes deadly, meteor showers, which also makes space traffic to and from the planet extremely dangerous – another reason why the planet is becoming uninhabitable.
In Star Trek Online, Praxis is presented as the former moon of the Klingon homeworld Qo'noS. After events that occur prior to the year 2409 broke the Khitomer Accords, mining on the remnants of Praxis renewed. The remnants of Praxis orbiting Qo'noS are collectively referred to as the Praxis Belt.