The Talosian system was a star system. The Talosian system was the primary star system of the Talos star group. This binary star system had eleven planets. The system was described as being similar to the Sol system by the crew of the survey ship SS Columbia in 2236. The fourth planet, Talos IV, was inhabited by a native species. The location of Talos was depicted on a Federation star chart in 2293. (TOS: "The Cage", "The Menagerie, Part I"; Star Trek VI: The Undiscovered Country)
By 2285, another planet in the system, Talos III, was a Federation colony (Star Trek II: The Wrath of Khan)
Background
Behind the Scenes
The Talosian system was at one point to have been a double star system. (The Making of Star Trek, pp. 93 & 96) Before production on that episode, Gene Roddenberry conceded that he was somewhat "at a loss [...] on exactly what it should look like," and further commented, "If it is too bizarre or confusing to the audience, we'll probably have to go back to a single sun." (The Making of Star Trek, p. 96) The map for the system showed two stars of equal size at the center of the star system; however, when the shore leave party was on the surface, it's not possible to see the suns as the sky was overcast.
The Explored Galaxy
This chart was also seen in several Star Trek: The Next Generation and Star Trek: Deep Space Nine episodes set in the 24th century, from the year 2364 to 2370. These were: TNG: "Conspiracy", "The Measure Of A Man", "The Emissary", "The Mind's Eye", "The Game" and DS9: "In the Hands of the Prophets", "Cardassians".
Star Trek: Star Charts
The system, known here as the Talos Star Group, was located in the Alpha Quadrant. This was a quadrinary star system. All four of the stars were M-class. The primary's magnitude was -3, which was 1,000 times brighter than Sol.
The name of the primary was Talos Prime (Talos A). It had a spectral class of M0IV, and its absolute magnitude was 0.1. The distance of the stellar companions of Talos Prime ranged from 175 to 650 astronomical units. These companions were named Talos B, Talos C, and Talos D. The system of Talos Prime had five planets, and one of them was an inhabited planet. (Pages 34, 37, 40-41)