“Blown away” is one of the most commonly used colloquial expressions Americans use to convey admiration or surprise.
Literally, it means “to be blown away by the wind,” but in actual use it can be understood as “deeply impressed,” “completely astonished,” or “overwhelmed.”
Depending on the situation, it conveys either positive surprise (impression, admiration) or a sense of being overwhelmed (something feels enormous).

3 everyday conversation examples
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I was completely moved by the performance. → I was blown away by the performance.
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I was really surprised by the gift you prepared. → I was blown away by the gift you gave me.
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The final scene of that movie was really shocking. → The ending of the movie totally blew me away.
3 academic/professional English examples
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I was deeply impressed by the precision of the research results. → I was blown away by the precision of the study results.
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The new data presented at the conference really surprised the audience. → The new data presented at the conference really blew the audience away.
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The innovative therapeutic approach truly impressed everyone in attendance. → The innovative therapeutic approach truly blew everyone away.