Kalachakra is a Sanskrit word that means "time wheel." In Tibetan Buddhism, Kalachakra is the name of a deity and also a system of teachings and practices leading to enlightenment.
The Kalachakra is a system of tantra yoga, which in Buddhism is to realize enlightenment through identification with tantric deities. These deities are not exactly gods and goddesses as understood in the West, but more like archetypes that representing the practitioner's own deepest nature.
As the name suggests, the Kalachakra is concerned with time (kala) and wheels or cycles (chakra). Many kinds of cycles are included, from cycles of time to cycles of planets to cycles of life. Kalachakra is associated with Tibetan astronomy and is the basis of the Tibetan calendar.
Kalachakra is said to be the most complex system of Tibetan tantra. In Tibetan mythology, the Buddha gave the teachings to King Suchandra of Shambhala, and it appears to have been introduced into Tibet in the 11th century CE. Today some form of Kalachakra is found in all schools of Tibetan Buddhism, but it is most prominent in the Gelug school.
Very broadly, there are three parts to Kalachakra --
Outer Kalachakra takes in the physical world. This includes the elements, earth geography, the measurement of time, the movements of stars and planets, and the beginnings and ends of universes.
Inner Kalacharka has to do with states of mind while awake or asleep. Some scholars equate inner Kalachakra with psychology.
Other Kalachakra is a path of practice that includes visualization of deities and meditation on mandalas.
Kalachakra practice is not a do-it-yourself project, but a system that requires the guidance of master teachers.