Digital Signatures
A digital signature is cryptographic proof that a message was approved by the holder of a specific private key and has not been changed.
In depth
When you send crypto, your wallet signs the transaction with your private key. Nodes on the network check the signature against your public key; if anything in the transaction was altered, or the wrong key was used, the check fails and the transaction is rejected. No password ever leaves your device.
Why it matters
Signatures are how a network confirms you — and only you — authorised a payment.