Discourse analysis is a method of ( usually) textual analysis, looking for the patterns in which information is presented, and using those to "decode" ( for lack of a better word coming to mind :$) the way in which information has been presented, and how arguments or discussions have been structured. In a general way, perhaps something akin to grounded theory coding--in that it looks past the face value of the written word to see what lies beneath.
There are different kinds of discourse analysis. There is political discourse analysis, rhetorical discourse analysis, and I think a branch even of historical discourse analysis, etc. You might want to find what branch your examiner has worked with. You might anticipate methodological questions from someone like this, so you may need to be prepared to distinguish between his methods and your chosen methods ( eg how did you analyse the content of your interviews? Have you provided a paper trail that shows the path of analysis?) and defend your methods as appropriate for your overall research aims.
Hope that helps!