What is the meaning of hot pursuit?

(DoD) Pursuit commenced within the territory, internal waters, the archipelagic waters, the territorial sea, or territorial airspace of the pursuing state and continued without interruption beyond the territory, territorial sea, or airspace. Hot pursuit also exists if pursuit commences within the contiguous or exclusive economic zones or on the continental shelf of the pursuing state, continues without interruption, and is undertaken based on a violation of the rights for the protection of which the zone was established. The right of hot pursuit ceases as soon as the ship or hostile force pursued enters the territory or territorial sea of its own state or of a third state. This definition does not imply that force may or may not be used in connection with hot pursuit. NOTE: This term applies only to law enforcement activities.