Some applicants prefer the shorter program option because they don't see the need for an internship (if they're not making a career change for example) & since it means less time away from the work world (which translates to one less year when you are forgoing a salary). A one year program can also be a good option for you if there's some kind of time pressure associated with your post-MBA goals. If you're returning to your current company or to a family business for example & want to be back in time to help lead a major project that's already slated, or if you're going into a field (like tech for example) where things are changing so quickly that you can make an argument for why one year is going to make a difference in your ability to achieve your goals & have the impact you want to have.
At the same time, many people value the two year option because it gives you the chance to do an internship (which can be especially helpful if you are making a career change). It also gives you more time to participate in clubs and conferences (which can give you good leadership experience & also help you build industry contacts) and because they just appreciate the slightly slower pace (not that b-school is a slow pace by any means) to make connections with classmates, take electives, etc.
Although most schools only offer the traditional two year MBA, a number of schools offer both the one year and two year options -- and if you do apply for the one year you'll want to be ready to explain why you need that accelerated pace.