This refers to the bitterness of a beer. Bittering of a beer is done by the addition of hops and it is the alpha acids in these little flowers that work the magic. IBU is measured using specialized tools like a spectrophotometer, however a high IBU does not necessarily mean a bitter beer.
"an Imperial Stout may have an IBU of 50, but will taste less bitter than an English Bitter with an IBU of 30, because the latter beer uses much less malt than the former. The technical limit for IBU's is around 100; some have tried to surpass this number, but there is no real gauge after 100 IBUs when it comes to taste threshold."
Sources:
http://beer.about.com/od/glossary/g/ibudefined.htm
http://beer.wikia.com/wiki/International_Bitterness_Units
"an Imperial Stout may have an IBU of 50, but will taste less bitter than an English Bitter with an IBU of 30, because the latter beer uses much less malt than the former. The technical limit for IBU's is around 100; some have tried to surpass this number, but there is no real gauge after 100 IBUs when it comes to taste threshold."
Sources:
http://beer.about.com/od/glossary/g/ibudefined.htm
http://beer.wikia.com/wiki/International_Bitterness_Units