The thought process behind the recurve blade is simple; it is much like a less pronounced version of the famous kuhkri-style machete. When a cutting medium, such as rope, comes into contact with the lower, narrower portion of the blade, the cutting stroke will force the medium across more cutting edge because of the widening of the blade towards the tip. It allows the knife to pack more cutting edge in a shorter blade length, and helps power the cutting medium along the edge.
Essentially, the widening of the blade towards the tip allows for the medium to come into contact with more edge during the cutting stroke.
It's sort of a murky explanation, but it's hard to render completely without being in person or having photographic examples of the cutting stroke.
I hope I helped---have a merry Christmas!