A condition where ordinary process must yield to immediate need. An emergency suspends the rules and must not be declared cheaply.
Latin emergere, ex- (out) plus mergere (to dip, plunge); a rising-out that will not wait.
Its root pictures something breaking the surface of water it was going under in: mergere is the same plunge behind submerge and merge. An emergency is exactly that, a condition that was under and is now surfacing too fast for the ordinary process to keep pace.