Since the months, or more in general time, was measured by observing the moon, Khonsu was considered to be lord of time, and also had tasks similar to those of Thoth, Seshat and Shai in determining the span of life of every being on earth, and similarly the number of years a king would be on the throne.
As a moon god Khonsu was associated with Thoth. But since the moon was also considered to be the nocturnal sun (the moon god being called "substitute of Re" in some texts) there was also a close relationship between Khonsu and Re, as well as between Khonsu (the son of Amun) and Shu (the son of Re), Amun and Re being associated closely in the New Kingdom.
Another association was with Harpokrates (both gods being children), and Khonsu was occasionally shown with attributes of Harpokrates on magical stelae and elsewhere (the sidelock of youth, or crocodiles under his feet). As a result Khonsu was also believed to be able to cure illness, possibly because someone whose health was lacking was believed to be under the influence of the moon.
Khonsu was especially worshipped in the Amun complex in the temple of Karnak.
He is usually depicted as a man with both the full moon and the new moon on his head. Sometimes he has the head of a falcon with the sun disk and two feathers.