A more thorough explanation:

A Municipal Corporation is a type of local government that is authorized by a state to administer local affairs. This can include establishing a police force, managing public services, and making decisions about local policies and regulations. Municipal corporations are created by a state's legislature and are given specific rights and powers.

For example, a city or town that has been incorporated by a state is considered a Municipal Corporation. The city or town has the authority to make decisions about local issues such as zoning, public safety, and public works projects. The city or town may also have a mayor or city council that is responsible for making decisions on behalf of the community.

In the case of Barnes v. District of Columbia, the Supreme Court ruled that the District of Columbia was a Municipal Corporation and therefore had the authority to establish a police force. This case illustrates how Municipal Corporations are given specific powers by the state and are responsible for managing local affairs.

Other examples of Municipal Corporations include counties, villages, and other types of local governments that have been incorporated by a state.