In usual parlance, when someone says "burn a CD" they are not talking about setting it alight -- instead, "burn" is slang for writing data to a Recordable/Rewritable CD (and, now, re/writable DVDs, too). It just sounds cooler than saying "make a CD" -- it gives the illusion of alchemy and pyrotechnics.
A blank CD-Recordable (aka CD-R) is more or less the same as a "pressed" (commercially mass-produced) CD in that it is the same physical size and has a spiraling grove on the highly reflective bottom side. It differs that this reflective side is not deposited aluminum like a pressed disc but instead some sort of organic dye. As well with a finished CD where will be "lands" and "pits" along the spiral groove, a blank CD-R has none.
Instead, a CD-R is totally reflective, and this is where the concept of "burning" comes in. Since the reflective layer is not metal but transtatic dye, its reflective properties can be changed relatively easyily -- at least in one direction, from reflective to non.
Some CD Burners use a separate laser, some just adjust the frequency and power but regardless of how they work, they work by changing the reflective property of a microscopic section of the spiral groove -- by, in effect, buring the dye material so it is no longer reflective. This is slightly different from a pressed CD where the non-reflective parts (the pits) are also "lower" than the reflective surfaces, the lands. A CD burner will use its laser in a precise pattern as to etch a coherent binary string into the entire 3 mile length of the groove.
A rewritable disc (aka CD-RW) varies slightly from a regular CD-R because while CD-Recordables are WORM (write once, read many), a CD-ReWritable can be physically erased and used over. Instead of organic dye, a CD-RW will use a phase-changing crystalline-metallic layer. Depending on the focus and power of the laser, pits can not only be created, but also removed by melting a micro-small section of the recording material which is then being cooled quickly enough to quench in its amorphous phase. If done right, that section of the recording layer will return to a reflective state.
Anyway, when you burn a CD, you are burning a "session" which is a segment composed of a "Lead in" area, where the TOC is stored among other things, the program area where the actual content (e.g. audio, data) is stored and the "Lead out", which signals the end of a session but doesn't store anything else really useful. The CD standard supports up to 4 sessions per CD, but usually you'll end up just doing one session that takes up the entire disc.
In addition to sessions, you also eventually have to "close", "finalize" or "fixate" the disc, a process which most importantly copies a finalized TOC to the standard TOC section of the disc and signals that no more sessions may be written. Before you close it, the TOC is stored in a section called the "Program Memory Area" where CD-Players and CD-ROM drives generally can't find it which is why, for all intents and purposes, you must close a CD before it can be used. | 
