the word premium is grossly overused. it should mean a quality dictionary word.com, geo, LLL.com/short name, etc.. but it is a very subjective situation.
Premium...
–adjective
10. of exceptional quality or greater value than others of its kind; superior: a wine made of premium grapes.
11. of higher price or cost.
A persons opinion of "premium" can vary greatly and is relative of the TLD, the person's portfolio, or the potential end user buyers. A "premium .com" may be of very different value than a "premium .info" or a "premium .ws". A domain may be described as premium for general use or just within a small market segment.
If I could create a useful domainers definition, I would say a Premium domain is one that someone looking for domains to develop would place in the top 10% list of domains they would find acceptable for their purpose.
A premium domain is basically a domain that's more valuable than a regular one, because it's short, easy to remember, made of a real word, or just sounds like an actual brand.