The Governor exercises executive powers in appointing the Chief Minister of the State and his Council of Ministers. He also appoints the Advocate General, the Chairman and the Members of the State Public Commission.
The Governor has formal legislative powers over the dissolving of the Vidhan Sabha and summoning of both the houses of the State Legislature. While exercising these powers he always has to act on the advice of the Chief Minister's Council of Ministers. A bill that has been passed by the state legislature will become a law after the consent of the Governor. Though he cannot reject a money bill, he can send back other bills for reconsideration. He doesn't have the authority to reject a bill for the second time.
The Governor uses his discretionary powers in certain situations. In the Vidhan Sabha elections if no party secures a majority the Governor has the authority to act on his own and ask the leader of the single largest party or the chosen leader of two or more parties to form the government. He then appoints that leader as the Chief Minister. Again when the state machinery breaks down due to improper administration the Governor can send a report to the President and ask him to impose President's Rule in the state.
The Governors cannot be impeached from office as the President.