From time to time I present MR concepts to people. I find processing tasks familiar to people and then map them to the MR paradigm.
Usually I take two things:
Group By / Aggregations. Here the advantage of the shuffling stage is clear. An explanation that shuffling is also distributed sort + an explanation of distributed sort algorithm also helps.
Join of two tables. People working with DB are familiar with the concept and its scalability problem. Show how it can be done in MR.