What were princely states?

Princely states, also known as native states, were feudatory states under a local or regional ruler in a subsidiary alliance with the British Raj

 There were about 565 princely states at the time of Indian independence in 1947 and about 562 of them were integrated with India through the efforts of Sardar Vallabhai Patel.

 For further reading check the following articles:

• Portuguese India
• British Raj
• Dutch Colonialism in India