exact meaning of run about
When I look it up in the dictionary that run about means to be very busy doing a lot of different things.
But there is a sentence that the boys run about, obeying the directions of a man with a whistle.
I am confused, I don't understand

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As per the comments - 'run about' is the same as 'run around'. It's not really a phrase, it's just two words - 'run', and 'about'. 'About' means something like 'in different directions'. 
The dictionary meaning you quoted is just an extension to that basic idea - If you are busy, you have to figuratively run from place to place to get things done.

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There is an interesting thing, the British usually say that, but I find that American say run around.

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I am not familiar with this phrase, we usually say "run around," instead.

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thanks~

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i guess that means: to move busily from place to place.
http://dictionary.reverso.net
or a person who roves around from place to place. 
http://www.thefreedictionary.com

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