For those of you who were (and still are) skeptical of Boeing's claim on the 1 Kw laser's ability to destroy an explosive or IED, here's more detail I got from them on how it was done.
Target munitions (IEDs, UXO) are destroyed by heating, resulting in a low-yield detonation. In other words, instead of exploding with their intended full force, the target munition "pops" or "fizzles" out, rendering it safe.
The optical system focuses the 1 kW laser into a "few cm diameter" spot at the target range. Within that spot, the average intensity is over 200 W/cm2. That intensity is approximately 20 times the average thermal output of a standard burner element on an electric stovetop. Over seconds or minutes of illumination time, that effect is sufficient to provide the thermal load necessary to detonate the targets used in the demonstration.