IBU or international bittering units is a measurement showing the actual, not perceived, bitterness that the alpha acids from hops have imparted on a beer. The strength, sweetness and maltiness of a beer impacts the way our taste buds perceive the alpha acid bitterness in the beer. Typically the stronger or maltier a beer tastes, the less we perceive the bitterness, so a brewer must balance the beer with additional hops or a longer boil time to compensate.
Below is a listing of common IBU levels that you can expect from different beer styles. The international bittering units are important when designing a beer as you want to make sure you do not add too many or too few international bittering units and create a beer that is not consistent with the style you are attempting to brew. Knowing the typical IBU of a style of beer may also be helpful when ordering a beer so that you can select a beer with a bitterness level that you find most enjoyable.