what makes a rewritable compact disc erasable and rewritable many times?

Answer 1

the surface that is writable to is meltable.
when you erase it - it is melted and resmoothed.
you can then rewrite to it
you can do this quite a few times before it breaks down and becomes unusable

Answer 2

First, You have to use CD/RWs.
Second, the CD/RW has to be "formatted" with the software that powers your burner.

I have a Samsung, which uses Nero, and a Dell, which uses DLA.

If you use the formatting utility, the CD/RW can be used a a floppy, however, it can only be read on your PC. If you want to take it to another PC, you will have to download your burner's "reader" program and put it on the other PC.

I did this before flashdrives. Now it is so much easier to use flashdrives. They have really come down in price and I suggest you consider investing in one or more.