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 ::
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 1's and 0's 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.