My account says that I have a premium subscription, what is that and will I have to pay to play after it expires?

Check the FAQ for the Premium perks: http://beastkeeper.com/faq

• Premium users can set Triggers.
• Premium users see maneuvers that are currently selected by your opponents at the Battlefield.
• Premium users get Inbreeding Warning when trying to breed pets that are close relatives.
• Normal users can perform searches only among pets which are being traded. Premium users can search among all pets. This can be useful if you're looking for a pet with special traits and want to buy it from another Keeper who didn't put this pet up for trade.
• Normal users only see a pet's mother and father. Premium users have access to full genealogy.
• Premium users can instantly leave the island from any point of the map. Normal users need to move to the portal tile frst.

Most useful in my opinion is the fact that you can leave the island from anywhere, you don't have to trek back to the portal to leave, secondly that you will always get a warning if you are about to inbreed by accident. And tied in with that, that you can see the entire lineage of a pet, not just the parents. Very useful and I usually try to keep premium actve, but it's not a gamebreaker if you don't have it. Right now I don't, and it's still ok. 

I checked FAQ I must have missed it.

Thank you for explaining it to me, I will try and keep up with the premium subscription :)