Arthur King was a time agent. He originally met the Doctor on an assignment by the Time Agency to hunt him down. He found the Doctor to actually fight evil, as they did on that assignment, fighting against the Sontarans. He found the Graak, an artificial creation of the Doctor's, to need a host. He volunteered, and the Graak became his symbiont. He also informed the Time Agency about the Doctor, and they called off the manhunt.
Arthur King would go on to become a good friend of the Doctor and The Engineer, helping them on numerous occasions. He would also go on to become a liason for the Time Agency, actually tricking the Doctor and the Engineer into their encounter with Magnus Greel. He would also inform them whenever history went wrong, by using his Time Agency wrist strap to look through the agency's records.
Little is known about King's role in the Time War. It is known that he served on the front lines as a soldier.
After the Time War, King would become a much more mysterious character. He barely ever revealed his past, only doing so to trusted friends. He has been known to be a flirt. He was also a good friend of Jack Harkness.
After the adventure with the Sycorax, he went back to the Time Agency, and found it destroyed. He then went looking for Captain Jack Harkness, who he found in the late 20th century. When Jack was promoted to leader, he became second in command. He continued to work with the Doctor. When Jack discovered this, he felt betrayed, but soon forgave Arthur. He is currently working on something in Torchwood,"something big."
Arthur King is a flirt, rogue, soldier, scientist, and spy. He often makes jokes.