Coffee berries grow on a tree and are picked when ripe. The part of the green coffee bean we want for the drink is actually the seed inside the berry. Getting the seed out for normal coffee, however, can be a time and labor intensive process involving slitting the berry and pushing the seed out.
Natural processing, on the other hand, involves leaving the berry out in the sun, often still on the coffee tree, and allowing the berry to essentially rot off the seed. This process is significantly less labor intensive and allows the coffee bean to take on a unique fruity flavor from the berry. Not the fruit flavor of subtle fruity undertones like many coffees, but a fruity flavor that almost tastes like a fruit infused coffee bean. As odd as it sounds, it is delicious!