Headroom means having good dynamic range. You can play a 10 or 20 watt amp and it will sound loud. But as you really dig in, you find it just loud...you can't get past that loudness. Headroom means you can be as loud as you need to be and still have some reserved power for those fleeting moments where it is REALLY loud.
Think of music with a very wide dynamic range...a symphony orchestra. There can be some VERY soft parts and some VERY loud parts. An amplification system that can replicate this well would have to have a lot of headroom to be able to play the softer parts at a pleasing and satisfactory level and still have the reserve power to deliver the very loud parts without clipping and creating lots of distortion.