2003 Odyssey-delay between gas/power: ideas?

Occasionally when attempting to accelerate from a stop, there is a delay between when I push the gas pedal and when the engine (I think) kicks in and produces power. Often, this results in a burst of speed, as I (or my wife) press the pedal a little harder reflexively when nothing happens. The delay can be as little as half a second or as much as a two seconds.

Any ideas you can offer would be appreciated. I'd rather not go to a mechanic before I have any idea what the problem is, and what is involved in the fix.