Non-repudiation service can be viewed as an extension to the identification and authentication service. In general, non-repudiation applies when data is transmitted electronically; for example, an order to a stock broker to buy or sell stock, or an order to a bank to transfer funds from one account to another. The overall goal of the non-repudiation service is to be able to prove that a particular message is associated with a particular individual.
In practice, proof with virtually 100% certainty, or undeniable evidence, is a difficult goal. In the real world, nothing is fully secure. Managing security is more concerned with managing risk to a level that is acceptable to the business. In such an environment, a more realistic expectation of the non-repudiation service is to be able to provide evidence that is admissible, and supports your case, in a court of law.