"Integral means comprehensive, holistic, inclusive, nonmarginalizing, embracing...."
An integral approach attempts to include as many perspectives, styles, and methodologies as possible within a coherent view of the topic. In a certain sense, integral approaches are 'meta-paradigms,' or ways to draw together an already existing number of separate paradigms into an interrelated network of approaches that are mutually enriching.
OK, so it's not so easy to understand at first blush, but neither is quantum physics! If you have an open and inquiring mind, check out these resources...