What is Exigent Circumstance?

Alternative Forms: Exigent circumstances
Legal Definition
An exigent circumstance, in the criminal procedure law of the United States, allows law enforcement, under certain circumstances, to enter a structure without a search warrant or, if they have a "knock and announce" warrant, without knocking and waiting for refusal. It must be a situation where people are in imminent danger, evidence faces imminent destruction, or a suspect's imminent escape. Once entry is obtained, the plain view doctrine applies, allowing the seizure of any evidence or contraband discovered in the course of actions consequent upon the exigent circumstances.
-- Wikipedia
Legal Definition
Exigent circumstances are exceptions to the general requirement of a warrant under the Fourth Amendment searches and seizures. Exigent circumstances occur when the a law enforcement officer has a probable cause and no sufficient time to secure a warrant.

Courts look at the time when the officer makes the warrantless search or seizure to evaluate whether at that point in time a reasonable officer at the scene would believe it is urgent to act and impractical to secure a warrant. Courts may also consider whether the facts suggested that the suspect was armed and planning to escape, whether a reasonable police officer would believe his safety or others’ safety was threatened, and whether there was a serious crime involved.

Exigent circumstances may also occur when the police is in hot pursuit of a suspect who is possibly involved in criminal activities and in the process of fleeing.
Legal Definition
These are the circumstances that exist in emergency situations where there is a serious risk to other people.