Premium domains are domain names that somebody else has already registered but that they are willing to sell. They cost anywhere from a few hundred to a few thousand dollars.
Premium domains are indicated by a gold star in domain search results. Pictured below, cup-cakes.com is a premium domain listed for sale at $1,577.00.
They likely include "generic" words that would be great for a particular kind of business (e.g. sandwich, dry cleaning). They also are likely to be shorter, more descriptive, more professional and more memorable than the regularly available names. Premium domains can help generate traffic and build brand awareness. Think of it as the same sort of investment you would make to trademark your company name or design a beautiful sign outside your shop.
You register them at the listed price just like you would any other name. After that first purchase, you can renew it at the regular pricing for as long as you choose to keep it.