(covers information from several alternate timelines)
Sherman's Planet was an inhabited planet in the Alpha Quadrant. The planet was located in the same quadrant as Donatu V, Deep Space Station K-7, and a Klingon outpost. (TOS: "The Trouble with Tribbles")
In 2256, this planet's location was labeled on the star chart "Alpha/Beta Quadrant Overview" in the ready room aboard the USS Discovery. (DIS: "Magic to Make the Sanest Man Go Mad", "The War Without, The War Within")
In the alternate 2259, before a colony could be founded on this planet, there was a dispute about the Organian Peace Treaty. This event was reported in a news ticker, which was in a collection of graphics and video media that were seen on a powerwall in the offices of Christopher Pike and Alexander Marcus at Starfleet Headquarters. (Star Trek Into Darkness)
Following the Federation-Klingon War in 2267, and per terms of the Organian Peace Treaty, ownership of Sherman's Planet could be assumed by the side that could most effectively develop it. The Federation's intentions for Sherman's Planet were to use it to cultivate quadrotriticale, a grain well adapted to the planet's climate. After the quadrotriticale was poisoned on Deep Space Station K-7, Starfleet diverted a freighter laded down with this grain to Sherman's Planet. The grain would be delivered a few weeks later than anticipated. (TOS: "The Trouble with Tribbles")
The Federation succeeded in best developing Sherman's Planet. However, by 2269, the planet had been struck by famine. On stardate 5392.4, the USS Enterprise, under Captain James T. Kirk, was assigned to escort two robot ships hauling an improved grain, quintotriticale, to the planet to alleviate the plight. (TAS: "More Tribbles, More Troubles")
In the 24th century, the formerly Lieutenant Commander Brannon Braga, a crewmember aboard the USS Enterprise-D, was born on this non-Federation world. In 2369, his birth planet was listed on the chart "USS Enterprise Personnel Database", which was displayed on a PADD used by Captain Jean-Luc Picard on aboard the USS Enterprise-D. (TNG: "The Chase", okudagram)
According to the book The Trouble with Tribbles and the Star Trek Encyclopedia (4th ed., vol. 2, p. 272), Sherman's Planet was named for Holly Sherman, a friend and college girlfriend of the episode's writer, David Gerrold.
According to the Star Trek: Star Charts (pp. 53, 57, 62, "United Federation of Planets I") and the Stellar Cartography: The Starfleet Reference Library ("Stellar Cartography", pp. 30-31; "Federation Historical Highlights, 2161-2385"), Sherman's Planet (Klingonese, "Sermanyu'q") (FGC-24187 V) was a M-class planet. The official name for the planet's government was the Sherman's Planet Joint Administrative Territory. The two capitals of this planet were Port Emily (Federation) and Ka'Hat (Klingon). There were 98.0 million Humans and 116.2 million Klingons living on this world in the late 24th century. This planet was on a disputed border with the UFP (2152-2267), and was settled according to the terms of the Organian Peace Treaty in 2267. In 2378, Sherman's Planet was listed as a Federation member. The primary FGC-24187 was a G-class star. According to a map of the Klingon Empire – prepared by the Scribe K'Tark for the Klingon High Council in the Year of Kahless 893 (2266) – Sherman's Planet was identified as a Klingon planet. This claim was propagandistic, as the Empire claimed many border systems and planets. This often put the Empire at odds with the Federation.
According to the novel Best Defense, the Klingon name for Sherman's Planet is Homog Three.
In Star Trek Online, Deep Space K-7 is in orbit around Sherman's Planet.