A few years ago when I first started this blog, I tried to write up a layperson's explanation of quantum computation. Anyone who works in the field of quantum computation has to come up with such a speal. My experience is that people get lost when I try to talk about quantum computers. Nowadays, I just tell them that I work on superconducting circuits: "We fabricate circuits on chips just like your computer chips and then we put the chips inside really cold refrigerators."
Michael Nielsen, a co-author of the standard quantum computation text, offers his less-confusing but sufficiently-complex explanation of quantum computation. The idea of visualizing the information as a list of numbers is a good idea. Maybe I can use Nielsen's explanation to tell people what I do, instead of simply saying that I work on superconducting circuits.