Izar was the place from which Starfleet Captain Garth was considered to have hailed. He was known as "Garth of Izar" during at least the 2260s. (TOS: "Whom Gods Destroy")
Background
Izar was most likely intended to be the Izar star system, also known as Epsilon Bootis. It was a binary star system (spectral classes K0II-III and A2V) about 200 light years away from Sol. If so, he would have either been born on or emigrated to one of the planets of that system.
Izar could also be a planet, nation, city, or town – the episode does not permit any conclusions in that regard. However, in "Metamorphosis", Zefram Cochrane was said to be "of Alpha Centauri", which was clearly meant as a star system. Since Cochrane was born on Earth, he must have emigrated there at some point and considered it his home; Garth may have done likewise from his birthplace (which was probably not Earth, as he refers to Humans as "Earth people"). Izar may also be a colony of Earth, as Garth appeared to be human (in the novels, this connection is made more clear, with Izar clearly a human colony).
According to Star Trek: Star Charts, on page 32, Izar was the name of the third planet in the Epsilon Bootis system. In 2183, the United Federation of Planets starship SS Horizon landed on the planet. Soon after, a colony was founded on this planet and, subsequently, was admitted into the United Federation of Planets. The colony was governed from the capital New Seattle, and there were 185 million humans living on the planet. Major attractions included the Starfleet Tactical School and the Izar Institute of Meteorology. This planet was located in the Alpha Quadrant.