The IBU's in beer refers to the International Bitterness Unit scale which is a standard for measuring the amount of hops in one's beer. For example, a hoppy beer like an IPA will have a very high IBU rating, like a 75, while a malty beer like a stout will usually (but not always) have a low IBU rating at around a 30. Really light beers will also normally have low IBU's. The most asked for draft beer in a bar in America is Coors Light and that beer has a rumored 10 IBU's rating. Any beer snob will tell you that hops are important. They add character, complexity, and flavor to your drink. It may be a little presumptuous to say, but without hops there would be no beer.
To be more specific, the IBU's in beer refers to the one part per million of isohumolone. Isohumolone is the acid found in hops that gives the beer its bite. In the beer industry people don't have sweet tooths, they have hop tooths. This means that people crave that bitter beer with a nice pungent taste to it. The IBU measurement is also helpful to people that don't like hoppy beers. For instance, some people will choose a dark beer like a black IPA, and assume it is going to be malty and sweet, only to be horrified by the bitterness they discover. If they had read the IBU's they would have known instantly that the IBU's were to high for them.
The truth is that all beers have IBU ratings, but they are mostly printed on menus at microbreweries. The reason for this is kind of murky, but microbreweries tend to attract beer snobs. So it only makes sense that this is where they will appear. It's always a good idea to ask your server how malty your beer is. The reasoning behind this is that while a beer does have an IBU rating, it also has a malty profile. The maltiness of a beer will obscure the crispness of the hop character in your beer. For example, a breakfast porter will have a nice sweet malty base, but in addition it will have a hoppy bite to it that will elevate the heaviness of what might normally be a very heavy beer.
The simplest way to think about IBU's is as a rudimentary guide to predicting what the beer your buying is going to taste like. Also, understanding and educating yourself about the beer you drink helps you taste the complexities that beer has. And finally, when you go into a brewery and bar, and you understand IBU's, the people that are serving you will just assume that you are an intelligent beer drinker.
Bartenders and servers are always trying to impress people who understand beer, and will more than likely give you free tastes of the other beers they have on tap. Talking about the IBU's in beer is a good conversation starter at the beginning of any night of drinking beer. It is also a good place to start in further educating yourself about all of the intricacies of beer.