He recalls the genesis from the "ambient social awareness" he gained by monitoring dispatch services in New York City. He says, "I just found this fascinating because you get this beautiful picture of what's going on in the city."
He calls Twitter a "personal news wire" and a "communications utility." But he cautions that it's not a social network... although one can be built on top of Twitter.
He also explains how Twitter gives you "super powers" though the example of making a mobile phone purchasing decision he made. Watch out Superman, here comes Twitter ;-)
Seriously, it's a great interview and gave me much better insight into Twitter. Check it out.