Most popularly, a Jeroboam is a wine bottle which holds four-fifths of a gallon (3.03 liters). It is named after Jeroboam I, a king of northern Israel.
According to Easton's 1897 Bible Dictionary, Jeroboam I was the son of Nebat and ruled "the people" (of Israel) from 976-945 B.C.E. The Bible credits him with the rebuilding and fortification of Shechem as the capitol of his kingdom. He later (had) built two golden calves at Dan and Bethel, the two extremities of his kingdom. Interestingly enough this was a bad thing not because of the icons, which were simply to signify the sacrifices made to God there, but because he called his people to sacrifice in these places rather than Jerusalem. You can read more about him in 1 Kings, starting at 1 Kings 12.
There is also a Jeroboam II, son and successor of Jehoash, who was the fourteenth king of Israel, serving from 825-784 B.C.E. His forty-one year reign was the most prosperous Israel had experienced. You can read about him starting with 2 Kings 13:13.
Easton's claims that Jeroboam means "increase of the people"; Hitchcock's Bible Names Dictionary claims it is "he that opposes the people". Given that both kings holding the name caused Israel to prosper (though the former is arguably an idolater in spite of raising the calves in God's name, and not to some "false" deity) the former seems more likely. Willard Espy claims that Rehoboam means "the clan is enlarged", but not being intimately acquainted with the language in question, I cannot say what that means for the translations of "Jeroboam". And finally, to shed some light on the former meaning (a bottle of wine holding 4/5 of a gallon) but further muddy the waters here; Douglas Harper's etymology Ja-Ju page (http://www.geocities.com/etymonline/j1etym.htm) says jeroboam - 1816, "large wine bottle," from Jeroboam, "a mighty man of valour" (I Kings xi.28) "who made Israel to sin" (xiv.16).. This is of course in reference to Jeroboam I who raised the golden calves.