A cover is essentially an envelope (it got it's name because it covers the contents), usually stamped and those stamps cancelled.

Here's some examples of fancy covers:

https://store.usps.com/store/results/collector-s-zone-first-...

According to https://en.wikipedia.org/wiki/Event_cover they are "decorated, stamped and canceled commemorative envelopes"

Essentially they are envelopes with stamps and a marking over the stamps that prevents the envelope and stamps to be used.

https://en.wikipedia.org/wiki/Cancellation_(mail)