From How CDs Work, you learn that a normal CD uses microscopic bumps to store data. The surface of the CD is a mirror, and the bumps disrupt the mirror's perfect surface. The laser that reads the CD can detect the difference between a perfect mirror and an imperfection caused by a bump because of the difference in reflectivity. By interpreting "perfect mirror" as a "1," and "bump" as a "0," it is easy to store digital information on a CD. The bumps on a CD are molded into the plastic when it is manufactured, so they are permanent.
To create a writeable CD (CD-R), you need to modify the surface of a CD so you can burn data onto it, turning it into a CD-R. There are no bumps on a CD-R. A clear dye layer covers the CD's mirror. A write laser heats up the dye layer enough to make it opaque. The read laser in a CD player senses the difference between clear dye and opaque dye the same way it senses bumps -- it picks up on the difference in reflectivity.
To create a rewriteable CD (CD-RW), you need a dye layer that can be changed back and forth between opaque and transparent. This page discusses the special material that CD-RW's use. The material has the property that it can change its transparency depending on temperature. Heated to one temperature, the material cools to a transparent state; heated to another temperature, it cools to a cloudy state. By changing the power (and therefore the temperature) of the writing laser, the data on the CD can be changed, or "rewritten."
A CD-R can be read by just about any CD player. CD-RW discs are not so versatile -- lots of older CD players cannot read them.
Here are some interesting links: