In the context of cryptography, authentication means "ensuring that the message you got comes from who you think it did".
Authentication is how we prevent the man-in-the-middle attack.
Authentication is one of the hardest parts of cryptography, because the only truly secure way to do it is by driving to the other party yourself to establish a pre-shared key so you can do message authentication code. Or to share your public key with them if you are satisfied with the safety of post-quantum cryptography.

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