The origin of the Kumbh is quite old and associated with Samudramanthan (churning of the primordial dea) and during the Samudramanthan Kalasha (pot of nectar of immortality).
Purana says that in the north of Himalayas, in the Khirasamuda, Devtas and the Asuras jointly conducted Samudramanthan. Mandar Parbat acted as Manthana Danda and Basuki Nag played the role of rope used in the manthan. Lord Bishnu took the avtar of Kurma and he took Mandar Parbat on his back. During the manthan process, one by one Puspak Ratha, Airabat hasti, Parijat Puspa, Koustava, Laxmi, Suravi and at last Dhanwantari came out with Amritakumbha. Dhanwantari handed over the Kumbha to Indra Devta. Indra then gave the custody of the Amrita Kumbha to his son Jayanta. Instigated by the Devta’s, Jayanta ran way with the kumbha towards Swarga. Asuracharya Sukra got very much annoyed with this and ordered Asura’s to capture the kumbha. War broke out between Devta’s and Asura’s. The battle lasted for twelve days and then the Devta’s were defeated. During this period, Devta’s hid the kumbha in four places which were Prayag (Allahabad), Haridwar, Ujjain and Nasik.
Since then, Kumbhamela is held at this four places. Since twelve days in Devlok is equivalent to twelve years in Earth. A Purna Kumbh takes place after every twelve years and a Ardha Kumbh after every six years.
Since Surya (Sun), Chandra (Moon) and Brihaspati were appointed to protect the kumbha during the battle. The holy snan (bath) is scheduled at the confluence of this three. It has been believed that if one can take a bath at the punya tithi, he will not have to take a rebirth as human and can avail mukti
There is a misconception that Kumbha Mela is held alternatively in these four places which is not true. Each place has its own Purna and Ardha Kumbh Mela.