A digital signature is a mathematical scheme for verifying the authenticity of digital messages or documents. A valid digital signature on a message gives a recipient confidence that the message came from a sender known to the recipient.
Digital signatures are a type of public-key cryptography, and are commonly used for software distribution,financial transactions, contract management software, and in other cases where it is important to detect forgery or tampering.
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In law, non-repudiation is a situation where a statement's author cannot successfully dispute its authorship or the validity of an associated contract. The term is often seen in a legal setting when the authenticity of a signature is being challenged. In such an instance, the authenticity is being "repudiated".
For example, Mallory buys a cell phone for $100, writes a paper cheque as payment, and signs the cheque with a pen. Later, she finds that she can't afford it, and claims that the cheque is a forgery. The signature guarantees that only Mallory could have signed the cheque, and so Mallory's bank must pay the cheque. This is non-repudiation; Mallory cannot repudiate the cheque. In practice, pen-and-paper signatures are not hard to forge, but digital signatures can be very hard to break.
View the full Wikipedia page for Non-repudiation