This is the technical definition of a "Digital Signature" as per the Information Technology Act, 2000. The process works as follows:
A hash function creates a unique, fixed-size digital fingerprint (hash) of the electronic record.
An asymmetric crypto system uses a pair of keys: a private key (kept secret by the signer) and a public key (freely available).
The signer uses their private key to encrypt the hash. This encrypted hash is the Digital Signature.
Anyone can then use the signer's public key to decrypt the signature and verify that it matches the hash of the document, thus authenticating the sender and ensuring the document's integrity.