I'll answer in the opposite order.
Dave said: I think I know what the crank is, but exactly what is the cassette? The 8 gears? Years ago, I don't remember it being called a cassette.
Yes, the cassette is the 8 speed gear cluster. You probably remember freewheels which screwed onto the hub and included the ratcheting mechanism. Cassettes are just the gear cogs and they slip over the freehub which includes the mechanism.
Dave said: Again, good news. Would it be a big deal, should the 8 speed rear fail, to upgrade the rear to a better gear set?
Replacing with better 8 speed components is as simple as buying and replacing. To move to 9 or 10 speed would require changing rear derailleur, shifters, cassette and chain. You might also need to change the chainrings or crankset and front derailleur, but maybe not. 8, 9 or 10 speed cassettes will fit on your freehub.
You can learn much at
Sheldon Brown's website.