The planet was located in the outer reaches of the Milky Way Galaxy, from where it took a hundred years for a radio message to reach the United Federation of Planets in the 2260s. (TOS: "A Piece of the Action")
In the mid-22nd century, the Iotian civilization was in the beginning stages of industrialization. In 2168, the starship Horizon discovered the planet and made first contact with the Iotians. The Iotians were found to be an extremely intelligent and imitative species. The first contact occurred before the Prime Directive was adopted by Starfleet.
When the Horizon left the planet, they left behind a number of textbooks and technical manuals on how to make radio sets and other similar technology. The book that became most influential was a text published on Earth in 1992, called Chicago Mobs of the Twenties. This text became something of a "Bible" for the Iotian culture for decades to come. The Iotian population completely mimicked their society on the criminal underworld of Prohibition-era Chicago, that was described in great detail in the book.
The Horizon was lost shortly after it left Sigma Iotia II. As a result of Chicago Mobs of the Twenties, cultural development on the planet stalled to the 1920s Earth level, as planetary resources were wasted on endless gang wars between the different territories.
In 2268, USS Enterprise came to visit the planet and to investigate the cultural contamination caused by the first contact, after the last radio messages of the Horizon were received by the Federation. In an attempt to manage the contamination and to steer the Iotian civilization to a more ethical path, Captain James T. Kirk of the Enterprise posed as a gangster and established a syndicate of the criminal organizations controlling the planet. He left Bela Okmyx, the Iotian crime boss of the Northside Territory, in charge and demanded an annual cut of 40% for the Federation. In reality, the 40% was to be put into the planetary treasury and used as a resource to guide the Iotians into adopting a more ethical system of government.
After the Enterprise left the planet, Doctor Leonard McCoy thought he might have forgotten his communicator on the planet. Spock noted that if the Iotians took it apart, they would have access to transtator technology, the basis for every important 23rd century Starfleet equipment. (TOS: "A Piece of the Action")
Background information Edit
After Captain Kirk introduced the Enterprise as a starship representing the Federation of Planets. Okmyx asked if that meant Kirk was from the same "outfit" as the Horizon. Kirk said yes, suggesting Horizon was in fact an early Federation ship. Another statement made by Kirk, that "the ship won't land, but we'll transport several people down.", suggests the Horizon may have been the type of ship that landed on the planet back in 2168.
According to the reference books Star Trek Concordance, Star Trek Encyclopedia, Star Trek Maps and The Worlds of the Federation and the Startrek.com article  as well as apocryphal sources such as the Decipher supplement Worlds, the FASA RPG source book The Federation the Horizon was the USS Horizon, that was later seen on screen as a desktop model in Star Trek: Deep Space Nine.
According to Star Trek: Deep Space Nine Companion, The original idea for celebrating Star Trek's 30th anniversary on Star Trek: Deep Space Nine was to have the crew return to Sigma Iotia to find the Iotians imitating the original series crew. It would have been a tongue-in-cheek to the "typical" Star Trek fan. The idea was dropped in favor of what became "Trials and Tribble-ations".
According to The Worlds of the Federation, the Iotians did in fact learn transtator-based Federation technology from McCoy's communicator. By the time a next starship arrived to the planet, the Iotians had built a Federation starbase-like installation in orbit and were all wearing Starfleet uniforms. By the 24th century, the planet had become a Federation protectorate. According to the comic "...Let's Kill All the Lawyers," however, the Iotians never touched McCoy's communicator for fear of angering him and eventually returned it to him decades later; the society was still modeled on Chicago's gangs but was more peaceful and law-abiding.
For the 2007 remastered edition of "A Piece of the Action", Sigma Iotia II was recreated with computer-generated imagery, making it appear as a more realistic and Earth-like planet.
According to the Pocket ENT novel Kobayashi Maru, the Horizon was the freighter ECS Horizon mentioned throughout Star Trek: Enterprise and seen in the episode "Horizon". The Horizon made first contact with Sigma Iotia II in the 2150s. The fate of the Horizon was unclear; by the end of the book it was deemed missing and presumed destroyed by Romulan action. This connection to the Original Series episode was also suggested by the set decoration of the ship in "Horizon", as a hard-bound copy of a book beginning with the title Chicago Gangs can be briefly glimpsed on a bookshelf in Travis' quarters aboard the ship.
According to the Star Trek: Starfleet Corps of Engineers short story "Fables of the Prime Directive", Sigma Iotia eventually joined the Federation after years of work behind the scenes by cultural specialists.