The Alpha Leonis system was an inhabited star system. Regulus was the primary of the system. Two planets were known to support life: Regulus III and Regulus V. Notable forms of life in this system included the eel-birds of Regulus V and the Regulan bloodworms. (TNG: "The Vengeance Factor"; Star Trek VI: The Undiscovered Country, production art; TOS: "Amok Time"; ENT: "Two Days and Two Nights") The system was located three hundred light years from the Bajoran system. (DS9: "Fascination")
In 2154, a Vulcan High Command attack fleet massed in this system in preparation for an abortive preemptive strike against the Andorians. Regulus was the closest accessible star known to be outside the maximum range of Andorian Imperial Guard listening posts. (ENT: "Kir'Shara")
The association between the Alpha Leonis system mentioned in "The Vengeance Factor" and the Regulus star and planets is based on reference material and the real world association. According to Star Trek Maps (pg. 29), The Worlds of the Federation (pg. 130) and Startrek.com, Alpha Leonis was the same system as Regulus. In the real world Alpha Leonis is the Bayer classification name for Regulus. 
According to the Star Trek: Star Charts (pgs. 56,61,62), the Regulus (also known as Alpha Leonis) system was located in the Beta Quadrant. It was a trinary star system. Regulus A was a B-class star with a magnitude of +1, which was a hundred times brighter than Sol. Regulus B was a M-class star. Regulus C was a K-class star. In 2152, this system was in non-aligned space. By 2378, the system had been incorporated into Federation space, and was a destination on the major space lanes.