If I didn't imply it clearly enough yet, The Martian is quite simply Robinson Crusoe in space. Sometime in the near future, manned space missions to Mars are possible (but not very frequent) and Mark Watney is a member of the latest expedition. Things go south and Mark is left for dead on the red planet. He has to "science the shit out of everything", as he memorably puts it, in both the book and the previously mentioned movie trailer. He grows potatoes on Mars, improvises a communication system to recontact Earth and comes up with all kinds of little details that make life on Mars just that much more difficult.
There is nothing much wrong with The Martian. It's funny, inventive and sincere in the same way that the movie Cast Away is; humans go on living because survival is second nature to us. The format of the novel, however, was a little rough around the edges. The material started out as a blog and was later put into print and this transition is sometimes visible. Problems arise and are solved so often that at the end I didn't feel that Mark's mission was dangerous. It felt like fiction and therefore some of the unforeseen consequences he encounters toward the end of the book seem tacked on.