The 'pound' of paper (paper weight) refers to (supposedly, though I think this is a loose rule of thumb) the weight of a ream of said paper.
The heaver the pound, the denser (typically, thicker) the paper.
20# paper is your typical copier paper.
80# and 100# are thicker/sturdier and (literally) 'heftier'. Most paper above 50# is considered 'card stock' and is suitable for things that require a more substantial presence.
So, in terms of 80# vs. 100#, 100# paper will be a bit heavier than 80# paper.
'Cover' is just a term to mean thicker paper--suitable for things like the cover of a paperback book or report. This is opposed to saying 'text' which is for lighter weight paper used for letterheads and the like.
'Matte' refers to the finish. It's not shiny, as opposed to say 'gloss' which would be a shiny finish.
Where things get confusing is that you can have 100# cover and 100# text. WHen you see weights like that, you can assume (but always check with your printer) that cover vs. text now refers to thickness. Both are heavy papers for their usage, but the cover paper will be much thicker akin to business cards.
Bottom line: Pick your paper by seeing the actual paper. Get samples from your printer before committing to a print run. In the end, it's going to be a personal decision as to what you think works best for the particulars of your project.