Hey there!

The Lefty's major benefit is in its rigidity, as well as how well it can handle a force known as "side-load."
For rigidity, the lowers are actually square shaped inside the uppers. This ensures that there is zero twist, or movement when coming into a rough section. In addition, having the dual crown attachment both above and below the head tube ensures there is no flex forward, or rearward during compression.

Side load is the effect that occurs when a rider puts force both straight into the ground, but has the fork on an angle such as if he were taking a bermed corner. Traditional forks use bushings to interface between the lowers and uppers, which due to the rubbers compression will lead to uneven force on one side of the stanchion. Not only will this wear the fork faster, but it also creates that "sticky" feeling that many forks are plagued with. The Lefty was specifically designed to not be affected by any of this!

It's also considerably lighter, and made of carbon fiber with double the service life of the equivalent Fox or RS fork!

Let me know if you have any more questions!