(written from a Production point of view)
According to the extensive background notes created by Robert Fletcher for the aliens of Star Trek: The Motion Picture, Fletcher established K'norm was the homeworld of the K'normians. (The Making of Star Trek: The Motion Picture, pp. 130)
According to Star Trek: Star Charts ("United Federation of Planets I" and "III"), K'normia (Psi Tauri) was the name of a star in the Alpha Quadrant. The primary was a Class F star. Magnitude of this star was +5, which was the same brightness as Sol. K'normia was the name of a planet in the system, too, and had, by 2378, become a member of the Federation.