An Exigent Circumstance is an unusual and time-sensitive circumstance that justifies conduct that might not be permissible or lawful in other circumstances.
For example, exigent circumstances may justify actions by law enforcement officers acting without a warrant such as a mortal danger to a young child. Examples of other exigent circumstances include protecting evidence or property from imminent destruction.
In US v Martinez, Justice Thomas of the United States Court of Appeal used these words:
“As a general rule, we define exigent circumstances as those circumstances that would cause a reasonable person to believe that entry was necessary to prevent physical harm to the officers or other persons, the destruction of relevant evidence, the escape of the suspect, or some other consequence improperly frustrating legitimate law enforcement efforts.”
In Alvarado, Justice Blackburn of the Court of Appeals of Georgia referred to exigent circumstances in the context of a drug bust:
“The exigent circumstance doctrine provides that when probable cause has been established to believe that evidence will be removed or destroyed before a warrant can be obtained, a warrantless search and seizure can be justified. As many courts have noted, the need for the exigent circumstance doctrine is particularly compelling in narcotics cases, because contraband and records can be easily and quickly destroyed while a search is progressing. Police officers relying on this exception must demonstrate an objectively reasonable basis for deciding that immediate action is required.”
All of the other answers were only detractors made up and not legal terms.
Reference(s) used for this question: Source: KRUTZ, Ronald L. & VINES, Russel D., The CISSP Prep Guide: Mastering the Ten Domains of Computer Security, 2001, John Wiley & Sons, Page 313. and http://www.duhaime.org/LegalDictionary/E/ExigentCircumstances.aspx