Dishwasher air gap - whatsit???

Moved into my house last September. Previous owners left all pertinent owners manuals except for the dishwasher. In this newsgroup, I've seen dishwasher air gaps mentioned a few times, and they're also discussed (badly) in a plumbing book I own. What exactly is the purpose of an air gap? How do they work?
I'm asking because my dishwasher has a little more leftover water than I think is normal after a cycle. The drain hose is clamped up as high as possible under the counter, which I understand is a good thing to do. (It drains into the sink disposal). Today, I'll be running the thing with a bunch of large beach towels nearby, just in case. :-) But, if sounds are any indication, the thing seems to be draining fine, so maybe I've just never noticed what the normal residual water level is.
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