Kevin D. Williamson captures the true essence of the appeal of Jon Stewart in a piece at NRO called The Destroyer Goeth:
Jon Stewart’s genius — “and for once that overused word is appropriate,” Aucoin of the Globe insists — is that he provides intellectually lazy people with an excuse for forgoing the hard work of informing themselves at anything but the most superficial level about political events. Human beings being what they are, there will always be an acute need for humor in our political discourse; Stewart’s contribution has been to substitute humor — and an easy, vapid, shallow species of humor at that — for the discourse itself, through what Jim Treacher deftly described as his “clown nose on, clown nose off” approach to commentary: When it comes to Obamacare, the minimum wage, or the national debt, you don’t have to get the economics as long as you get the joke.
It's easy to laugh along with the crowd as Stewart smugly mocks politicians and pundits (the vast majority of his targets being conservatives of course). It provides the pretense of both being informed of the latest political news while also being smarter than those on the receiving end of the mockery. There's no need for deeper knowledge or understanding of any of the issues as long as you're in on the joke.