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Think of it as a SHA-1 or an MD5 that is generated using a private key, and can be verified using the public key (and the content of the data that was signed).

It verifies that the signer had access to the private key, and that the data signed by the private key is the same data that you are verifying with the public key.

It's like the other checksums (SHA-1/MD5/etc) with the addition of identity verification (so long as you can trust that the private-public keypair used to sign it is only accessible to parties you trust).

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