It has become clear what Cameron means by this. The aim is to get rid of the public sector altogether and replace it with, initially, organisations which are cheap because they use free labour on the front line; with co-operatives of former public sector workers which will soon be swallowed up or ousted by private companies; and with "social enterprises" which are very little different from private companies. Local authorities will be stripped of even more powers, and will dwindle away.
Is it giving power back to the people? Emphatically not. At the moment people have a right to services, which are paid for out of taxation. As Karl Marx said (and I'm not a Marxist!): To each according to his need, from each according to his ability. The Big Society means it will be pot luck whether you have any services at all, and those you have will be delivered for profit. There will, of course, be plenty of "volunteers" to keep things running; the redundant public sector workers.