The Prime Minister rejected criticism that the concept was "too vague" and a "cover for cuts", insisting it was central to the "social recovery" the country needed.
In a speech to social entrepreneurs in London, he said: "This is my absolute passion.
"I think it's a different way of governing, a different way of going about trying to change our country for the better, and it's going to get every bit of my passion and attention over the five years of this Government."
Mr Cameron described the Government's deficit-reduction programme as only his "duty".
He went on: "What is my mission, what is it I am really passionate about?
"It is actually social recovery as well as economic recovery, and I think we need social recovery because as I've said lots of times in the past, there are too many parts of our society that are broken.
"Whether it's broken families or whether it's some communities breaking down or whether it's the level of crime, the level of gang membership, whether it's problems of people stuck on welfare unable to work, whether it's the sense that some of our public services don't work for us, we do need a social recovery to mend the broken society and to me that is what the Big Society is all about."
He said people needed to "take more responsibility" and "act more responsibly".
The Government's response to any problem was only ever "half the answer", he said.
Summing up the aims of the Big Society, Mr Cameron said: "What this is all about is giving people more power and control to improve their lives and their communities.
"That, in a nutshell, is what it's all about."
There has been growing criticism of the Government's attempts to broaden the role of the voluntary sector at a time when public services are under intense pressure.
But Mr Cameron sought to tackle critics of the Big Society head-on.
"Some people say it's too vague," he said.
"Well, if they mean by that there isn't one single policy that's being rolled out across the country, well yes, I accept that because actually what we are talking about here is a whole stream of things that need to be done."
It involved a combination of devolving power to local government, opening up public services and encouraging more volunteering and giving, he said.
"Then people will say 'OK, maybe it's not so vague, I can see you've got the three parts to it, but this is just a cover for cuts, isn't it? You're just doing this because really you want to do cuts'.
"I mean, I've been talking about this for the last five years as leader of the Conservative Party, I was talking about it when public spending was going up, I will be talking about it when public spending is flat and I will talk about it when public spending is going down.
"It is not a cover for anything, it's a good thing to try and build a bigger and stronger society, whatever is happening to public spending."
But he added: "Isn't it better when we are having to make cuts in public spending to try and encourage a bigger and stronger society at the same time?
"If there are facilities that the state can't afford to keep open, shouldn't we try to encourage communities who want to come forward and help them?"
The Prime Minister acknowledged that other people warned that the cuts would make the Big Society more difficult to achieve.
"What I would say to that is, of course there is no area that should be - can be - really immune from the public spending problems that we face.
"But if you actually look at what central government is doing, the part that I'm responsible for, we are actually doing things to try and make a bigger society more possible."
Mr Cameron said that £200 million from the banks would be put into a new Big Society bank this week.
A £100 million transition fund is being set up to help charities and social enterprises bid for Government contracts to provide services.
The training of 5,000 community organisers is also to be announced this week.
Mr Cameron admitted that the ideas underpinning the Big Society were "not entirely new".
But he added: "My question is, should we try to do more of it?"
Former prime minister Tony Blair, asked about the Big Society, told Sky News today: "We will wait and see what it actually means."
TUC general secretary Brendan Barber said: "The most worrying thing about the Big Society is that Prime Minister truly believes that policies of slash, burn and sack will make all our lives better, and not just for those for whom he is planning tax cuts.
"The logic of this is that his ideal society is Somalia where the state barely exists, and his hell the Scandinavian societies that the rest of us admire for combining quality services, equality and dynamic economies."
Shadow Cabinet Office minister Tessa Jowell said: "David Cameron can try as many relaunches as he likes.
"It doesn't change the fact that by cutting too far and too fast, and hitting the charities and community organisations that do so much to support volunteering and social action across the country, it's David Cameron who is undermining what he likes to call the Big Society."
Answering questions from his audience, Mr Cameron acknowledged that his administration's cuts programme would affect "important" parts of society and would make the Government unpopular.
"The truth is that everyone is having to make cuts - central government, local government - and it is incredibly difficult," he said.
"It is not possible to make those cuts without cutting some things that are important. That's the situation we are in as a country."
He added: "The duty of this Government is to deal with the economic mess that's been left. We have got to deal with that deficit, we have got to make these cuts, we have got to put up these taxes.
"It will not make us popular. It will make us unpopular. It will make me unpopular.
"I recognise it is my duty. We've got to do this for the good of the country. We've been left a mess, we've got to clear it up.
"But I don't believe it is impossible to do your duty at the same time as having a sense of mission and purpose about what would make this country stronger, better and a nicer place to live and make our communities more healthy.
"I think that there is an enormous appetite for that. People do believe that we need a social recovery as well as an economic recovery.
"This would be the right thing to do, whether we were increasing public spending or cutting it, whether the economy was growing or not growing."
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