Digital signatures ensure the authenticity of documents by providing a cryptographic method to verify the signer's identity and the integrity of the information. When a document is signed digitally, a unique hash is generated, which is then encrypted using the signer's private key. This creates a signature that can be validated by anyone with access to the signer's public key. In this way, digital signatures prevent forgery and unauthorized alterations, ensuring that the document has not been tampered with. They play a vital role in securing online transactions and facilitating trust in electronic communications.