Briefly, the advantages are:
1. No till. The mulch covering creates a worm habitat that keeps the soil soft and workable
2. Almost no watering. The woodchips help keep the soil from evaporating water
3. Almost no weeding. The chips block seeds from ever getting to exposed soil
4. No fertilizing or sprays. Chemicals are a no no, and the decomposing chips add the complete spectrum of nutrients to the soil. Also healthy plants resist disease and insects on their own, so no need for chemical sprays.
It's pretty straightforward. Cover your ground with some newspaper or cardboard to kill off any grass/weeds, then add a 6 inch layer of compost or soil. Finally add 4 inches of woodchips on top and you are done. You can add 6-8 inches for berry bushes, or 12-16 inches in an orchard.
However, what makes this system work better than any other is how well it supports mycorhyzal fungi. Fungi are well supported by woodchips, which form relationships with plant roots, which effectively act as steroids to your plants. You can see in the first video how oversized his plants are.
Also, only ever use heirloom, open pollinated seeds. The system boils down to woodchips and open pollinated seeds.
The results speak for themselves. The inventor of this method has been doing it for 40 years, and lives completely out of his garden. His system is so abundant that he grows 80% more than he needs, and feeds the rest to his chickens or guests.