The M1911 is a semi-automatic, magazine-fed, recoil-operated handgun chambered for the .45 ACP cartridge, which served as the standard-issue side arm for the United States armed forces from 1911 to 1985. It was widely used in World War I, World War II, the Korean War, and the Vietnam War.
In the Anime
The M1911A1 pistol belongs to George Miyagusuku who has been using it throughout his wartime as he is an ex-US military. It is likely he kept the weapon after leaving the military. He is shown to be drawing the weapon out during flashback scenes of Saya awakening. He was about to fire but could not bring himself to do this to the innocent looking girl in front of him.
When George is attacked, Kai steals his father's M1911 pistol to try to chase down the chiropteran who wounded his dad. He fires the whole magazine at the chiropteran but the rounds have little effect as the chiropteran is capable of regenerating. David confiscates the gun from Kai. Later, David returns the pistol to Kai to show that he feels Kai had matured enough to handle it.
Kai had little knowledge of handling firearms but after Riku's death and Red Shield HQ's destruction, he constantly kept on practising his aim with the M1911 until he becomes proficient with it. Kai uses it as his primary weapon for the remainder of the series.