Yellowstone is thought to be above a mantle plume, of with there are tens to hundreds on our planet, although there is plenty of debate on this matter. The exact nature of mantle plumes is a huge area of hotly contested research, but generally the are thought to be large melts originally sourced from the D'' layer (core / mantle boundary). Below the park, the plume is theorized to have resulted in magmatic intrusions overlain by a hydrothermal system. The intrusions can also be considered as magma chambers of a supervolcano, which has had several ultraplinean caldera-forming events.
The Yellowstone hotspot is the only obvious expression of a mantle plume beneath the continental United States, which may be why you consider it "unique." The other major plume / hotspot in the US is Hawaii.
Yellowstone is certainly not the only major geothermal area in the world; geothermal areas in New Zealand, Italy, Japan and Antarctica are comparable in terms of heat flow. It's unclear what you mean by "thermal power" but Yellowstone park does not have any geothermal electric power generation plants. New Zealand, on the other hand, generates 13% of their national power needs geothermally.