An International Bitterness Unit (IBU) is the measurement of the bitterness in beer. One IBU is equal to one milligram of isomerized alpha acid per liter of beer. Isomerized alpha acids are the main bittering compound derived from hops. One IBU is measured directly using a formula with a spectrophotometer and solvent extraction.
There are three different equations that a home brewer can use to estimate utilization and IBUs without needing a spectrophotometer and solvent extraction. The equations named after the men who invented them are: Rager, Tinseth and Garetz. The equations are different in how they estimate the utilization percentage. Rager is most often used when you are brewing with extract and partial mash. The Rager equation takes original gravity of the boil into account, and tends to produce IBU estimates that are on the high side of the three equations. Tinseth is often used by all-grain brewers, or brewers that do full batch boils. It generally produces lower IBU estimates than Rager, but is considered very accurate. The Garetz equation is the least popular of the three methods, but generally provides estimates somewhere between Rager and Tinseth.
The longer you boil your hops the more bitterness and IBUs you will add. Late addition hops, boiled for 5-10 minutes, add very little bitterness and are used primarily for aroma. Bittering hops are usually added for the full boil time of 60 to 90 minutes.
A malty beer, even with a high IBU may taste less bitter than another less malty beer with a lower IBU. Because the apparent bitterness of a beer is subjective to the taste of the drinker and the balancing malt sweetness of the beer IBUs are not always an accurate measure of the hoppiness of a beer. Generally speaking a beer with IBUs of less than 20 will have little to no apparent hops presence, a good example of this would be a Wheat beer. Beers with IBUs from 20 to 45 are the most common and have mild to pronounced hops presence, an American Pale Ale or Pilsner would usually fall in this range. Beers with IBUs greater than 45 are heavily hopped and can be quite bitter, such as your typical India Pale Ale.