If you shoo away a bug, or shoo away an animal or a person, you're waving your hands at them to tell them to go away and leave you alone. You might even say "Shoo!" or "Shoo-shoo!" If a bug lands on your cheeseburger, you can shoo it away. If you're talking on the phone and your little siblings run up to you and try to grab the phone away from you, you can shoo them away, too.
You might shoo pigeons away from your balcony, if they're making loud noises and pooping everywhere. "Shoo-shoo! Get away!" you might shout.
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This guard is shooing chickens away from the subway:
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Usually, you shoo someone away from you. But you can also shoo someone in another direction that you want them to go. When you shoo someone, you're waving your hands at them to show them where to go, almost as if you're pushing them that way. A mom might shoo her kids into the car. A dad might shoo his kids away from a hot pan on the stove. You could shoo your friends up to your room when they come over. But if you just shoo someone, you're telling them to go away.