What is spine decompression therapy, and how does it work exactly?

Doesn't. I suspect you are referring to a variety of computerized machines that purport to reduce herniated discs. These machines go by various names which i will not mention here. They are basically fancy traction machines. The treatment is very expensive and despite the hype have never been shown to be effective. They are usually not covered by insurance.
Traction. It is essentially traction of the spine. It is meant to pull the spine segments apart so that the disc might heal. There are many ways to accomplish this including physical therapy techniques, specialized machines often used by chiropractic, and inversion tables. There are no good studies on any but the techniques may have some benefit. Inversion is likely the cheapest.