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Original sentence is given below!

The world has been holding its breath to see how Americans vote. Would they choose to stay on the same path and elect John McCain, a Republican, or would they choose to vote for change and for new policies, and elect Barack Obama? With the USA the only real superpower in the world, whoever they choose affects us all.

here, what does the word breath give the context meaning?
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The idiom of "holding [your, its, my, etc.] breath" means waiting with great anticipation.

It also has a partner: Don't hold your breath. That means "Don't expect it to happen any time soon."

A: Jim said he's pay you back the money he owes you next week.
B: Really? Well, I'm not holding my breath. He's said that every week for the last two months.
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There is an idiom "hold one's breath", and it basically means "be anxious, worried or excited (about something" or "be in an anxious, worried or excited state of anticipation (about something)". The expression refers to the fact that normal breathing can be interrupted when someone is in such a state (anxious, worried or excited).

So, you might reword the sentence this way: "Everyone in the world is anxiously waiting to see how Americans vote."

EDIT:
Oops! I'm far too slow for GG. Emotion: big smile
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Comments  
Thanks a lot Grammar Greek..
 Yankee's reply was promoted to an answer.
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thank you very much Yankee