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Imagine waving your arm back and forth in a bunch of water. It takes a lot more work than waving your arm in air. You have to move the water out of the way as you move back and forth. You have to do similar, but less, work to move the air out of the way when waving. You usually don't notice because it's a smaller amount of work, and in daily life it's always there. You're used to it.
As you pointed out though, there's no air on the moon. That lack means something moving doesn't have to use energy to move air out of the way. The flag waves because the astronauts who planted the flag touch it and make it shake. It then continues to wave longer than we expect because there is no atmosphere to dampen the motion. It does eventually stop waving because the bending and unbending of the fabric in the flag also dissipates energy.
This question, as well as several other moon-mission related oddities, was investigated by the show MythBusters. A clip is currently online showing an experiment they conducted in a vacuum chamber (check out http://tinyurl.com/btb3sw). Like the folks in the show, keep asking good questions about the world(s) around you.
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