LiveCoding is the act of programming under real-time constraints, for an audience, as an artistic entertainment.
I enjoyed a little taste of it when I demo'ed the writing of some components of a web-application in Visual Studio.NET using VJ#, in front of an audience of about 50 colleagues, during my internship at Microsoft. Fixing the errors as I went along coding in front of the people, made the exercise very interesting.
But live coding is much more than that. Live coding is the activity of writing (parts of) a program while it runs. Check out feedback.pl that is a text-editor that has two threads, one runs the text-editor and the other runs the code that is being edited in the text-editor. When Ctrl-X is pressed, the code written re-parses itself, leaving the values of all variables intact. Now, imagine a DJ in a night-club, composing music in front of a live audience in the dance hall by writing code in Perl using feedback.pl. That is what LiveCoding is all about!
I think, dealing with parsing and runtime errors in a graceful fashion is the primary issue in LiveCoding systems.
Visit TOPLAP to know more about LiveCoding. TOPLAP is short for: Temporary|Transnational|Terrestrial) Organisation for the (Promotion|Proliferation|Permanence) of Live (Algorithm|Audio|Art|Artistic) Programming.