Your description is about right, except that they are usually more than "a little strap" since they have to be holding on to your waist as you run. It would be quite unpleasant, not to say chafing, to have one's fuel belt moving up and down with every step.

You can see lots here:
http://www.teamestrogen.com/product/...0-c90-c92.html

There are a few different brands, Fuel Belt and Nathan being the main ones I see out there. I have a Nathan Speed 2 which I like, but I only wear it for running more than an hour. On shorter runs, I don't need to drink. But keep in mind that I a heavy drinker (of water!) the rest of the day and that I live in a cool climate. I don't find it terribly uncomfortable, but I'd rather run without the added bulk/weight.