Put simply, boosting the incomes of the poor and the middle class can help raise growth prospects for all.
150616-growth income inequality IMF chart
One possible explanation is that the poor and the middle class tend to consume a higher fraction of their income than the rich. If more money flows to these segments of society, they will consume rather than save, raising demand and spurring aggregate growth in the short run. What this means is that the poor and the middle class are key engines of growth. But with inequality on the rise, those engines are stalling.