To be unable to reject the validity of a document (unable to prove it is counterfeit). The term is the opposite of "repudiate," which means to reject the validity of something.
Digital signatures and certificates provide non-repudiation because they guarantee the authenticity of a document or message. As a result, the sending parties cannot deny that they sent it (they cannot repudiate it). Non-repudiation can also be used to ensure that an email message was opened (see email tracker