A humble programmer is one who creates programs (for a living or out of interest) and is aware of the fact that it can be done more elegantly, better, simpler. Briefly: humble about this business of programming.
Outlined in possibly the most important chapter in Steve Mc Connell's Code Complete - Chapter 33: Personal Character (p821):
"...programming is an attempt to compensate for the strictly limited size of our skulls. The people who are best at programming are the people who realize how small their brains are. They are humble."
Originally from Edsger Dijkstra's "The Humble Programmer (www.cs.utexas.edu 
).
See original on c2.com