Butler was James T. Kirk's pet dog, a Great Dane, whom he had at his house at least in 2284, and who died in 2286.
Upon being pulled into the extra-dimensional realm known as "the Nexus" in 2293, Kirk was able to experience a number of settings from his past, including being reunited with Butler. (Star Trek Generations)
In the script of Star Trek Generations, Captain Kirk's dog was named Jake. According to Ronald D. Moore in the audio commentary for the Generations DVD, William Shatner changed the name to Butler on the set, after a recently deceased dog of his own.