The term “cover” goes right back to the very start of the postal service. It was another word for an envelope. When the Victorians first started sending letters, they wrapped them up in paper (the “cover”) and wrote the address on that. In 1840, a Penny Black was stuck on a cover to put in the post and cancelled on that day. This was the start of the “first day cover” and they have been collected ever since.
We still use the word “cover” to refer to a collectable envelope. Of course, more specifically there are two types of cover: first day covers and commemorative covers.