For me, Burning Man is an opportunity to consider alternatives. As we live in a society that (to its detriment) increasingly values homogeneity of thought, appearance and action, Burning Man is a breaking of that pattern--a whole city full of people who value and celebrate diversity. The contribution of each participant comes from a personal place, and is not externally determined (apart from the "weak and idle" theme). This is the freedom people I think people are talking about--you feel more free to be who you really are at Burning Man because there is no status quo.
Burning Man challenges me to think about alternative ways of living, not only as an individual, but as a community. Based (or at least more focused) on different values than everyday society, Burning Man challenges me to think critically and creatively about use of materials and conservation, the challenges of volunteerism and participation, teaching and the communication of culture, the importance of building and sustaining relationships, and the role of individual responsibility in all of this. While I would not say that Burning Man changed my ways of thinking about these concepts, it provided the venue and the catalyst for the solidification of my approach as well as some genuine epiphanies that have led to real change in my everyday life.
Also, burning shit is a lot of fun.
It's not that I hate you. It's just that I'm a much better person than you.