"Integral" means comprehensive, inclusive, balanced, not leaving anything out.
Strange as it sounds, most human activities are not integral—they are instead partial, often fragmented, frequently broken. Although integral approaches do not have all the answers, they do attempt to ask more interesting questions, and perhaps even point in the direction of real solutions—whether in work, play, education, international politics, relationships, life....
At this very time, there is something of an "integral revolution" occurring around the world, as all the old and partial approaches are being questioned, and new and more integral responses are being explored.
If you also want to pursue the more detailed aspects of integral approaches as they are now being pioneered, please see http://www.integralinstitute.org.