An exclusive licence is a licence, which gives someone the exclusive right to do one or more of the things reserved to the copyright holder, and must be in writing, and for a prescribed term. It precludes anyone else, including the author, from using the work, without permission. The same exclusive licence cannot be given to two different people, but there could, for instance, be different exclusive licences to translate the same work into different languages.
(Source: Introducing Copyright: A plain language guide to copyright in the 21st century)
A non-exclusive licence may be written or verbal, or may be inferred from conduct, and may be revoked at any time at the author’s discretion, subject to conditions in Clause 22 (4) of the SA Copyright Act.
There can be a number of non-exclusive licences given for one work. For instance, a writer may assign to one publisher the right to publish the work in the USA, and to another publisher the right to publish in the UK and to a third, the right to translate the work into another language. Ownership in the rights is retained by the licensor e.g. author, so only certain rights are licensed to the third party for a certain period or for the full copyright term, as the case may be.
(Source: http://www.svw.co.za/copyright)
Authors have the choice whether they want to enter into a 'non-exclusive' licence or an 'exclusive licence'. Authors may retain certain rights, e.g. to place a copy on an institutional repository and/or personal blog; use of their works in teaching or for research; translation rights, etc.