Why are hashes in the bitcoin protocol typically computed twice (double computed)?

[Bitcoin]

Why are hashes in the bitcoin protocol typically computed twice (double computed)?

According to the wiki specification of the bitcoin protocol, hashes are typically "computed twice". For example:

hello
2cf24dba5fb0a30e26e83b2ac5b9e29e1b161e5c1fa7425e73043362938b9824 (first round of sha-256)
9595c9df90075148eb06860365df33584b75bff782a510c6cd4883a419833d50 (second round of sha-256)

What is the reasoning for this? I imagine it somehow provides additional security, or protection against potential attack vectors, but I can't reason what those attacks might be.

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