It is the slightly fictionalized story of Christopher McCandless who, upon graduating from Emory in 1990, struck out for a life on the road, cutting himself off from friends, family, and, as far as he could, from civil society. Without going into detailed spoilers, things don't end well. But it's a fascinating journey right up until the end. It's very long, about two and a half hours. But it held my attention all the way through.
The movie was written and directed by Sean Penn, based on a book written by Jon Krakauer; given Penn's tedious self-seriousness and lefty politics, I was prepared to dislike it. So I was pleasantly surprised. McCandless's quest takes him to scenic places, and he meets a number of interesting people. He takes himself and his offbeat philosophy way too seriously, but he's affable enough about it. And, more importantly, the movie distances itself from him just enough; we can reject his outlook without rejecting the movie too.
You can read Krakauer's original story for Outside magazine about McCandless here. If you haven't already done so, I recommend reading it after watching the movie. If anything, the real story adds details that make its ending more tragic than the movie's.