Ok, so in the most basic sense, there are three stories going on that converge together near the end of the album. We know very little about the outside world at the beginning - we know that the power has gone out for some reason, and it's been off for years. There are vague allusions to Nuclear fallout. Most people are dead.
1. THE BAND. Four musicians cooped up in a bomb shelter manage to avoid whatever horrid catastrophe has ended the world. They embark upon an "unplugged tour," since their electric guitars no longer work, and go from city to city playing music and looking for more survivors. Most of the story is told within the framework of their "broadcast" - they are able to rig up a radio transmitter and extend their reach. There are even commercials for post-apocalyptic products ("Flaman's Quality Environment Suit Emporium!" and "Artificial Sunshine.")
2. JULIET. One of the first people that the band meets up with is a six-foot-tall warrior woman wielding a machine gun. She's on a mission to a fabled survivors' colony on the east coast, but the band already knows the bad news - it doesn't exist. Unhappily settling into a quieter life, Juliet soon gives birth to a son named Adam. It's unclear exactly who his father is. Soon afterward, Juliet commits suicide and her funeral is interrupted by the violent climax of the story.
3. MORRIS & THE GRAVEDIGGER. Sergeant Hank Morris is a warlord who has risen to fill the power vacuum. He exterminates gang leaders, and installs puppet governments to do his bidding. His personal army, the 40th Regiment, is the dominant force in the area. He's obsessed with being revered, respected, and even worshipped, believing that he has saved us from our own destruction.
This puts him into direct conflict with the Gravedigger - a mysterious legendary figure that is beginning to inspire religious fervor as well. Supposedly, the Gravedigger gives a final resting place to those who have no one else to bury them. He is a comfort to many, and a threat to Morris. It is never actually confirmed whether he exists.
THE ENDING. On his quest to kill the Gravedigger and become a God, Morris tracks down the Band - he's heard their broadcast and believes them to have information on his rival. Before he can complete this mission, the 40th Regiment turns on Morris - his deputy shoots him in the stomach and leaves him to die. He threatens the band, he screams for help, he refuses to apologize for anything he's done - and yet, the Gravedigger comes for him anyway. The Gravedigger will bury anyone who has no one.