Doctor Manhattan (Crudup), aka Jon Osterman, has a PhD in atomic physics from Princeton. During his research, he ended up becoming trapped in a test chamber and his body was torn to pieces by the force of the atomic generator. Over the next few months, his body reformed itself until he was a normal man again — except that he glows ultraviolet.
After that, he became an instrument for the US government, helping us win the Vietnam War. He eventually rebelled from this use and wanted to end humanity, but Laurie persuaded him not to. At the end of the movie, he departs Earth altogether.