Live coding is coding as performance. Matt alerted me to a Impromptu which is a programming language designed for sound coding performances. There is a gallery of sound performances and code at the site to give an idea of what the live coders might be typing to get what effects.
Live coding would seem to be connected to realtime coding competitions like live coda when the coding challenge is performative and the competition environment can be witnessed as a performance.
Pedagogically I wonder if live coding is more effective than write-compile-run coding. Certain languages like Ruby have live coding environments that let you type commands and see the results immediately. What is different here is the idea of language created for live coding in a performative context.