Digital signature
A cryptographic proof that a message was created by the holder of a private key and has not been altered.
In simple terms
You sign a hash of the message with your private key. Anyone with your public key can verify it.
Analogy
A handwritten signature that is mathematically impossible to copy onto a different document.
Going deeper
Signatures give authenticity, integrity and non-repudiation in one primitive. Ed25519 (used by SSH and modern protocols) signs with a single pass of Curve25519; verification is cheap enough to run on every certificate and firmware image you load.
Common mistake
A signature is not encryption — the message stays readable. Also: never reuse a nonce in ECDSA; bad nonce selection has leaked private keys in the wild.