When you burn a disc, you write data on it. If you were taking an SAT test, the analogy would look something like this:
Hard Disk : Write :: CD/DVD : Burn
The reason the term burn is used is because the CD-writer, or burner, literally burns the data onto a writable CD. The laser in a CD-writer can be cranked up to a more powerful level than an ordinary CD-ROM laser. This enables it to engrave thousands of 1s and 0s onto a CD.
So that is why people talk about burning songs or files to CDs. They could just say they are writing the data to a CD, and it would make sense, but people seem to think burning sounds cooler.
* These videos are coming directly from Youtube, they may or may not be most relevant to the word "Burn"
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