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I still don't understand what a cover is. Is it the cancellation stamp?

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:

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.