Digital signatures are electronic stamps that can be used to identify the sender or the signer of a digital document. Think of digital signatures as the digital equivalent of the signature placed on a contract or a check. Digital signatures use public and private key pairs to ensure the authenticity of an electronic document. The creator of the document will have the private portion of a digital signature scheme which is encoded onto the document when it is signed. Then the recipient of the document would receive the public key of the digital signature scheme. This would allow the recipient of the document to know that the document was authentic and really did come from the sender.
Keeping with a paper document analogy, the purpose of a signature is to verify that the signer is the originator of the document. Sometimes documents require signatures in person to have a witness to the signature. The public key/private key pair allows electronic documents to be verified in much the same way.
A digital signature scheme generates a key pair, and the public key will only match the corresponding private key and vice versa. This ensures that the document which contains the private key is authentic and has not been changed since signing.
One thing to note is that a digital signature is altogether different from a digital certificate, which verifies content on a website with a third party. A digital signature is also very different from an email signature. While an email signature is a digital representation of the senders name and contact information, it does nothing to guarantee the origin of the message or document.
E-mail messages can be signed with digital signatures to verify their origin just like other electronic documents. Using digital signatures will allow recipients of these documents to feel comfortable in trusting that the document really came from the listed sender. This process can also help guarantee that the document has not been modified since being sent.