A local government is a form of public administration which, in a majority of contexts, exists as the lowest tier of administration within a given state. The term is used to contrast with offices at state level, which are referred to as the central government, national government, or (where appropriate) federal government and also to supranational government which deals with governing institutions between states. Local governments generally act within powers delegated to them by legislation or directives of the higher level of government.

- Local Government, Wikipedia as on 9th January, 2018

Since 1992, local government in India take two very distinct forms. Urban localities have Nagar Palika but derive their powers from the individual state governments, while the powers of rural localities have been formalized under the panchayati raj system.

- extracted from Local self-government in India, Wikipedia as on 9th January, 2018

'Deriving power', in this case, means that the areas within which the Nagar Palika can execute its powers, and what those powers are, are fixed by the State Government.

Got any questions?