George Kirk was a Human Starfleet officer in the early 23rd century. His father was Tiberius Kirk. George was the husband of Winona Kirk and the father of James T. Kirk and George Samuel Kirk. (TOS: "Where No Man Has Gone Before", "Operation -- Annihilate!", Star Trek)
In 2233, at the age of twenty-nine, Kirk was serving as first officer aboard the USS Kelvin under Captain Richard Robau. (Star Trek, Star Trek Beyond) His wife was also aboard the ship and was pregnant with James Kirk at the time.
James Kirk often spoke of his father, crediting George with providing him with the inspiration to join Starfleet. George lived at least long enough to see his son become captain of the USS Enterprise in 2265. (Star Trek)
Background information Edit
George Kirk was played by Chris Hemsworth.
In the script of Star Trek, George Kirk was referred to as a thirty-two year-old as of 2233, suggesting he was born in 2201. The script also described him as having an "all-American face."  On the other hand, James Kirk muses in Star Trek Beyond that upon reaching thirty, he'll be a year older than his father when he died, making George twenty-nine at the beginning of 2233, with a corresponding birth year of 2203 or 2204.
As director of the film Star Trek, J.J. Abrams specifically asked for Chris Hemsworth to portray George Kirk, though the actor had only been working in America a few months beforehand. He received notification of the role one day after he returned to Los Angeles following a couple of months of filming in Chicago. "I had a phone call from my manager saying that I needed to drive across right away to Paramount Studios and meet J.J. Abrams in his office to do the scene," Hemsworth explained. "I cancelled what I was doing, drove over there, did the scene in his office at his desk and he said, 'Fantastic – we have to work together. You start next week.' And that was it!" Although Abrams didn't share much information with the performer at that time, Hemsworth did use a genuine scene from the movie for his audition. He had very little time to prepare for the role, though there wasn't a lot he could do to ready himself for the part anyway. (Star Trek Magazine issue 145, p. 91)
Since this character had never appeared before, Abrams and Hemsworth were free to collaborate on the portrayal of George Kirk. "On set we discussed how we wanted to play it," remembered Hemsworth. "J.J. had very specific ideas about what we wanted to achieve, but he's also the kind of director that gives you the freedom to try other things and put your own interpretation on it. It was more a case of taking the scenes that we had, and finding the truth in what was being said, then just playing that and trusting in the overall picture J.J. was creating and that the writers had done for us." (Star Trek Magazine issue 145, p. 91)
Constructing a backstory for his own character, Hemsworth came to the opinion that George Kirk is "someone who has quite a strong sense of justice. He's that old-fashioned kind of good guy: he has strong morals and puts other people before himself. But he was also played as someone in his mid-20s. He's still quite young, so I think a lot of who he is was ingrained, maybe through his upbringing. I feel like he had a pretty strong sense of character, and especially to be put in the position he is at such a young age says a lot about who he is." (Star Trek Magazine issue 145, pp. 91-92)
In many ways, Chris Hemsworth was relieved that, because there wasn't much rehearsal time, he didn't have long to consider what he was letting himself in for by playing James Kirk's father. "That was funny," he remarked. "In a really good way, I was thankful for not having enough time to think about it, because the turnaround from the audition to when I was shooting was so quick. I didn't have too much time to think about the pressure that was built around it. But afterward, the more I heard about it, I started hoping I did an okay job! [....] There were a couple of times when I was sitting there on set, and I thought that it doesn't get any bigger than this, in terms of money, expertise and everything that's put into making a film. And I wondered what I was doing there! But [...] it was mind-blowing and exciting." Also, Hemsworth found his confidence regarding his performance was boosted by Abrams. (Star Trek Magazine issue 145, p. 92)
Although Spock referred to George Kirk as being a lieutenant when he was aboard the Kelvin, Kirk actually wore the rank braids of a lieutenant commander; Spock may have been abbreviating his rank in a non-traditional manner (lieutenant commanders are usually afforded the privilege of being referred to, in short, as commanders and not as lieutenants). Shelby, Geordi La Forge and Deanna Troi have both also been addressed as lieutenant, despite clearly holding the rank of lieutenant commander.
George Kirk was mentioned in the unfilmed Star Trek: The First Adventure script as having died when his craft, the Bonaventure, disappeared during an experimental dilithium-fueled warp jump. Montgomery Scott worked with him on the project.
He may have a brother, since James T. Kirk said he was staying at his uncle's farm in Idaho in Star Trek Generations. It was never made clear which of his parents had a sibling though, or if he was just using the term for a long time family friend. In Star Trek, an uncle Frank was cut from the script and reworked into Winona's new husband heard in the film.
The name "George" for James Kirk's father first originated in Vonda N. McIntyre's TOS novel Enterprise: The First Adventure, which gives his full name as "George Samuel Kirk, Sr". The novel Collision Course calls him "George Joseph Kirk", while the comic story "Captain James T. Kirk: Psycho-File" calls him "Benjamin Kirk". Star Trek II: Biographies calls him "Eugene Claudius Kirk".
Intel's Star Trek tie-in website gave his serial number as SA-733-9624-AM.
George Kirk was seen as the first officer of the USS Enterprise under Captain Robert April in the novel Final Frontier. In the novel, Kirk was the one responsible for convincing Captain April (who had been charged with naming the as yet-unnamed ship) to name the ship Enterprise. The cover art for the book contained a picture of him - and it bears a clear resemblance to Hemsworth, even though the actor was only four years old when the book was published.
Additionally, Kirk played a major role in the novel Best Destiny, where he was once again shown as first officer under Captain Robert April. He plays a more direct role in 16 year old James Kirk's life, and is upset with him for his rebellious behavior.
IDW Publishing's comic Keenser's Story depicts him as having been present for first contact with the Roylan's (Keenser's people). After Keenser helps them fix their shuttle, he befriends George on the ride back to the Kelvin, having chosen to go with him with the intention of signing up for Starfleet Academy.
The novel The Autobiography of James T. Kirk lists George's birthday as December 13, 2206.