Below is probably as accurate a definition as I’ve ever seen.
The Army National Guard as currently authorized and organized operates under Title 10 of the United States Code when under federal control, and Title 32 of the United States Code and applicable state laws when under state control. The Army National Guard may be called up for active duty by the state or territorial governors to help respond to domestic emergencies and disasters, such as those caused by hurricanes, floods, and earthquakes, as well as civil disorder. The District of Columbia Army National Guard is a federal militia, controlled by the President of the United States with authority delegated to the Secretary of Defense, and through him to the Secretary of the Army.
Members or units of the Army National Guard may be ordered, temporarily or indefinitely, into the service of the United States. If mobilized for federal service, the member or unit becomes part of the Army National Guard of the United States, which is a reserve component of the United States Army. Individuals volunteering for active federal service may do so subject to the consent of their governors. Governors generally cannot veto involuntary activations of individuals or units for federal service, either for training or national emergency. (See Perpich v. Department of Defense .)
The President may also call up members and units of the Army National Guard, in its status as the militia of the several states, to repel invasion, suppress rebellion, or enforce federal laws. The Army National Guard of the United States is one of two organizations administered by the National Guard Bureau, the other being the Air National Guard of the United States. The Director of the Army National Guard is the head of the organization, and reports to the Chief of the National Guard Bureau. Because the Army National Guard is both the militia of the several states and a federal reserve component of the Army, neither the Chief of the National Guard Bureau nor the Director of the Army National Guard “commands” it. This function is performed in each state or territory by the State Adjutant General, and in the District of Columbia by the Commanding General of the District of Columbia National Guard when a unit is in its militia status. The Chief of the National Guard Bureau and the Director of the Army National Guard serve as the channel of communications between the Department of the Army and the Army National Guard in each state and territory, and administer federal programs, policies, and resources for the National Guard.