From a "nuts and bolts" perspective, debates are important because at all other times, the things they say are separated by time and space, making mudslinging and misrepresentation easier than when you are face to face. In a debate, the public gets to hear/read the candidates answer the same questions and respond directly to each others' statements and accusations.
This is also part of the reason debates favor the challenger: Obama has a record to run on in addition to a vision for the future. So there are a lot more facts (pro and con) people can look at to base their decisions on and it is a lot harder to misrepresent who/what he is. For example, you don't have to wonder (nor is it even relevant anymore) what his vision for healthcare is; he got an actual law passed that people can judge without having to ask him what it means. Romney has only his claims about what he wants to do, so selling his candidacy is more about arguing hypotheticals about the future than showing facts about past performance.
A little more concise: The challenger can attack the record and the vision of the incumbent, but the incumbent can only attack the vision of the challenger.
Romney also had the added need to shift the focus of his campaign from his recent gaffes.
At the same time, Evo is right: because re-elections are mostly a referrendum on the job performance of the incumbent, more votes are decided earlier than in an election where both candidates are new (and on equal footing). This means that debates often don't matter. If the record of the incumbent is great, he'll win (the election), if it's terrible, he'll lose. So in order for the debate to matter, you need a specific set of conditions, including a muddled record resulting in a small lead for the incumbent and a challenger who wins the debate by a lot. And that's what we have. So yes, debates often don't matter, but this one matters more than any in the past several decades.
Also, one does not need to watch the debate to be affected by it. Everyone who checks today will read/hear - from virtually every news outlet - that Romney won big. Hearing someone else tell you who won (and by how much) can be as effective, if not more, than seeing it for yourself.
And how big of a win was it? According to CNN, 2/3 of respondents said Romney won, the largest percentage since they started asking the question in 1984, by a healthy margin.
http://politicalticker.blogs.cnn.com/2012/10/03/cnn-poll-romney-wins-debate-by-big-margin/?hpt=hp_t2
So there will almost certainly be a bounce from this. We'll have to wait and see how big it is and if it has any persistence.
