Premium domains are the high quality domains. They describe the content of the website and are easy to remember. For example, programmerforum.com is a premium domain.
Whether the domain is premium or not is up to the domain register to decide. And the decision is completely arbitrary. There are no strict criteria for whether or not the domain is premium, so at the end of the day, the premium factor is determined by how much people are willing to pay for it.
Websites with premium domains usually take higher positions in the search engines, because they contain keywords. Also, the userbase of such websites tends to be bigger, because users remember the name and come back more often.
How to find out if the domain is premium?
The best way would be to check its price. Usually domains are around $30, so if you see a higher price — you might be looking at the premium-domain. Although there may be exceptions — for example, the domains in the .na zone are simply ridiculously expensive, without any notion of premiality.
There’s no limits to the cost of the domain — it can easily get into thousands, or even dozens of thousands dollars. Also, more often than not, premium domains are sold by the resellers, who lucked out and registered a good domain. In this case, there can be absolutely any price.
In order to find out the cost of your domain, head to https://www.estibot.com/. Take note, that this is not a definite price and more of a suggestion.
Are the premium domains worth the cost?
It depends on your ambitions. If you want a small blog where you write down your personal experience — you do not need a premium domain. But if it is a huge portal with a huge marketing budget and a goal to dominate the sphere — premium domain will help you achieve leadership much faster.