Into the Wild is the story of a well-to-do young man who gives up his worldly possessions to carry out an adventure living in nature. In many respects, it has elements of books like Thoreau's Walden, although Chris McCandless (unlike Thoreau) dies in the end.
How does McCandless reject society? American society seems to center around the idea of the American dream -- of going to college to get a good job, to buy a house, to buy a car, etc. McCandless fared well at Emory, a top university, and seemed well on his way to achieving that dream. However, he seemed troubled by the materialism with which he was raised and the problems that wealth and the acquisition of wealth caused in his own family.
In the end, he did what few others in his position would do. He "rejected society" by giving away what our society puts a strong emphasis on -- possessions. He gives his money (roughly $25,000) to charity and even burns the money in his wallet. In this way, he rejects the societal values of property and the American dream in pursuit of a higher ideal in nature.
Hope this helps!