There are two important reasons why Kumbh Mela is held in India .
One is based on stories in scriptures and another is a practical reason. The
practical reason is that Kumbh Mela is meant for the great minds in Sanatana
Dharma (Hinduism) to meet and discuss and share knowledge for the welfare of
the living beings. Decisions and new findings in philosophy and science taken
during the Kumbh Mela are then carried by the saints to different parts of the
world.
Reason in Puranas
To obtain the Amrut, the Devas had to churn the Milky Ocean .
Mandara
Mountain agreed to be the churning rod and Vasuki, the serpent agreed, to be the rope. To churn the ocean the Devas needed the help of Asuras as the Devas could only hold one-end of the rope. But Devas were not willing to share the Amrut with Asuras. Finally, without any other choice the Devas agreed to share the Amrut with the Asuras.
Reason in Puranas
The most important and widely accepted reason in scriptures
is found in the Bhagavad Puran. Puranas are filled with wars between Devas
(demigods) and Asuras (demons). The Devas always have the upper hand but
occasionally due to some curse or misdeeds the Devas lose this upper hand. Lord
Indra, the king of Devas, was once cursed by Sage Durvasa and as the result of
this curse, Demons overpowered the Devas.
To find a solution the Devas approached Lord Vishnu. Lord
Vishnu advised them to obtain Amrut - ‘the nectar of immortality.’

Mountain agreed to be the churning rod and Vasuki, the serpent agreed, to be the rope. To churn the ocean the Devas needed the help of Asuras as the Devas could only hold one-end of the rope. But Devas were not willing to share the Amrut with Asuras. Finally, without any other choice the Devas agreed to share the Amrut with the Asuras.
Churning started and the ocean started to yield divine
gifts. Amrut was the last to appear. Dhanvantari, the physician of the gods,
appeared with Amrut. The Asuras took the Amrut and ran away. A fight between
the Devas and Asuras ensued.
All the stories associated with Kumbh Mela are the same till
this point. But the story changes from this point in different scriptures.
First Version
In Skanda Purana, it is suggested that Indra’s son Jayanta
got hold of the Amrut during the fight between the Devas and Asuras. He ran
away with it. The demons started to chase Jayanta around the earth. The chase
lasted for 12 days or 12 human years. One day of devas is equal to one human
year. During this time, the nectar spilled at Allahabad ,
Haridwar, Nasik and Ujjain . Thus a Kumbh Mela
is held in these spots once in 12 years.
Second Version
This legend of Kumbha Mela appears in Vishnu
Purana, Brahmananda Purana, Padma, Agni Purana, Mahabharata and Ramayana.
It suggests that as soon as Dhanvantari appeared with Amrut, Lord Vishnu passed
it to Garuda – the vehicle of Lord Vishnu. Asuras chased Garuda for 12 days or
12 human years. And Garuda stopped or the nectar spilled at Allahabad ,
Haridwar, Nasik and Ujjain .