In law, Domicile is the status or attribution of being a permanent resident in a particular jurisdiction. A person can remain domiciled in a jurisdiction even after they have left it, if they have maintained sufficient links with that jurisdiction or have not displayed an intention to leave permanently (i.e., if that person has moved to a different state, but has not yet formed an intention to remain there indefinitely)

This is the definition as per Wikipedia.

In simpler words, domicile, is a way to find if a person belongs to one state or not.

So that any benefit that is given by the state government will be provided to that person and not to any one from any other state.

All states have a limited budget for education, employment, health, ration etc. So how can a state ensure that not the entire population of India is trying to reap the benefit of a scheme that is funded by one state only for those who are permanent resident of that state.

To prove that a person is the permanent resident of a particular state, there are a few rules.

1. If you were born in a state, you automatically get the domicile of that state
2. If your parents are born in a state and have their proof of domicile valid, the children automatically get domicile
3. If you have lived for  7 =>years in a state, you get its domicile
4. If you have done class 11 and class 12 from a state, you get its domicile automatically ( varies from state to state)
5. If your parents (even one of them) are working for the Defense for 1 year and you have done class 11 & 12 from that state, you are eligible
6. If your parents have worked for the state government for 2 years and you have done your class 11 and 12 from the state, you are eligible to get the state domicile
7. If you own a land / property in a state, you may get domicile (varies from state to state)

Kindly read the links below in detail to find the state domicile you may be interested.

Other states domicile will be added as and when I find them.

References:

Maharashtra Domicile

Karnataka Domicile 1 

Karnataka Domicile 2

 Andhra Pradesh Domicile 1

Andhra Pradesh Domicile 2