In Harry Potter, why did they need Wands? Like, in prisoner of azkaban when Harry got angry at his aunt or whatever, and then blew her up, he didn't have a wand, so, why do they need one?

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Wands
In Harry Potter, why did they need Wands? Like, in prisoner of azkaban when Harry got angry at his aunt or whatever, and then blew her up, he didn't have a wand, so, why do they need one?