Essentially the non-executive director’s role is to provide a creative contribution to the board by providing objective criticism.
The 1992 Cadbury Report initiated a debate about the main functions and responsibilities of non-executive directors. Today, it is widely accepted that non-executive directors have an important contribution to make to the proper running of companies and, therefore, more widely to the economy at large.
http://www.iod.com/intershoproot/eCS/Store/en/pdfs/roleofnxds.pdf
As the Cadbury Report said, they: “should bring an independent judgement to bear on issues of strategy, performance and resources including key appointments and standards of conduct.”