John Baez wrote several introductions to that theme, e.g. <a href="http://arxiv.org/abs/math/9802029" title="Baez' intro">here</a> or the discussion with further links <a href="http://golem.ph.utexas.edu/category/2008/10/categorification_in_new_scient.html" title="n-cat cafe">here</a>. (Mazur's article is very good too!)