What is management quota? What is the process of selection through management quota?

As said in other answer it means seats withheld by the management of the college. They have the right to admit anyone on these seats regardless of the entrance exam etc. That is, of course, a method to earn more.

Management quota is just another name of donation. You can get admission in your choice of college by giving donation. Almost all the private institutions have some percentage seats reserved for management quota.