The basic idea is that there is a huge amount of surplus time available for thinking and other activity, but which has mainly been soaked up by television - perhaps a trillion hours a year, Shirky says. It is available for productive enterprises or, for that matter, something like lolcats, he says ("an image combining a photograph of a cat with text intended to contribute humour", according to Wikipedia).
You can watch Clay Shirky talk about cognitive surplus, and the concept is taking off. Naturally it hasn't won over everyone - Nicholas Carr regards the web as hastening the domination of our lives by media we consume rather than create. He gives the example of a short video showing a boy sticking his fingers in his little brother's mouth, which has been viewed 211 million times. Not to mention lolcats. But I guess Carr is saying that the cognitive surplus is being wasted, not that this must always be the case.