(covers information from several alternate timelines)
Omicron Ceti was the primary of its star system. In orbit of this star, there was the inhabited planet Omicron Ceti III. After a failed attempt at colonizing this planet in the 2260s, the Federation would successfully attempt again and, by the mid-24th century, the colony was thriving. (TOS: "This Side of Paradise"; TNG: "Eye of the Beholder")
In 2366, in an alternate timeline, during the Federation-Klingon War, the location of Omicron Ceti was labeled on a tactical situation monitor in the ready room aboard the USS Enterprise-D. (TNG: "Yesterday's Enterprise", okudagram)
In the real world Omicron Ceti is also known as Mira. In the Star Trek universe however, the name Mira is used as an alternative shorter name for the red giant star Mira Antlia of the Mira Antliae system visited by the Enterprise-D in TNG: "Conspiracy".
According to Star Trek: Star Charts (p. 37) and Stellar Cartography: The Starfleet Reference Library ("Federation Historical Highlights, 2161-2385"), the Mira (Omicron Ceti) system was located in the Alpha Quadrant. In the late 24th century, this was a Federation system.
A lost Federation colony on the fourth planet, Omicron Ceti IV, was seen in the comic book story Old Loyalties.