A pilot declares this (like declaring an emergency) so he can proceed direct to his destination and drink beer at the bar ASAP because if he is delayed at all, he legally can't drink because he has to fly early the next morning (pilots may not drink any alcohol during the 8 hour period before flying).
Pilot: Delta 1965 declaring a beermergency and proceeding direct Portland.
ATC: Delta 1965, I understand you are declaring a beermergency. Cleared direct Portland. Do you need any other assistance?
Pilot: Delta 1965 also requests maximum forward speed.
ATC: Delta 1965, approved as requested.
When the beer supply in any type of social drinking situation becomes critically low, and replenishment is either impossible or extremely dificult. Thus creating a major buzzkill. Symptoms of a beermergency may include, panic, chaos, premature sobriety and all the girls/guys at the party becoming ugly again.
When we realized that we were critically low on beer, we knew we had a real beermergency on our hands.