An unfinished beer. It can be in a bottle, can, or keg cup. A jersey beer is usually a forgotten beer that was then inefficiently replaced by a new one, and left on a table, countertop, etc. They can also result from a person not forgetting, but being unable to finish said beer. They are more often associated with parties, not bars. That is due to the likelihood of running out of beer at a party versus a bar, and the ability to pass out, resulting in unfinished beers. The discovery of wasted beer in the morning, which was much needed the previous evening, is the reason to use the term, with negative overtones. Earliest usage circa 1977.
Those frat boys act cool, but I have never seen more jersey beers after a party, what a bunch of clowns. Look at all the jersey beers! What a waste.