Dry shampoo is not exactly the same as what you're describing, fatfrog, as it's not a product that starts out dry and then gets wet, but that stays dry start to finish. You sprinkle the powder into your hair, let it sit for a few minutes (I actually leave it in while I shower, under a shower cap), and then brush it out. You're left with nice fresh-smelling hair, and a great deal more volume, as you've brushed out a lot of oil and you've left behind a small amount of powder, particularly at your roots where the volume increase is more apparent.
So, you don't have to re-dry or re-style your hair (although you can use a curling iron or flat iron for touch-ups). Saves me time, and means that I carry less in the way of "wet" grooming products. I don't use hotel toiletries, in large part because I find the scents objectionable.