The world's gone to pieces. People just trying to survive. Many people have "half-life" now, as they have some sort of illness or diseases (like cancer) that will kill them while they're young, and some just have genetic defects.
Max is just surviving, Citadel leader's (Joe's) folks, hunt him down (nothing personal, they do this to other people as well) hoping he becomes useful to them, and he did, he was a universal blood donor who is healthy (aside from the mental issues). He becomes a bloodbag for one of these sick people (what a lovely day guy - Nux). The blood transfusion helps him become healthier but it's not a cure.
Joe withholds water to rule over people. he thinks of himself no less than a god to all the people at citadel. The warriors he employs are sick, have little time to live, and are willing to risk their lives because they've been promised heaven. This is why they say "witness" before doing an act that they think will result in their death. They are doing it for Joe, and want to make sure someone is there to witness that act so that the gates of heaven will be open to them. That's how he's built up his army. His relationship with his wives is not consensual, and he had them locked away without any hope of escape. They are just "breeders" there for his pleasure and to give him a worthy offspring that can take his place when he dies.
Furiosa, along with her mother were kidnapped when she was a child. Her mother was killed 3 days after. All the stuff that she's done for Joe has finally taken a toll, and seeing the way Joe's wives were, she decided to do something now that she strong enough, to redeem herself, which means sneaking Joe's wives away to her home, which as far as she remembers, was pretty much like heaven on earth to her. The green place.
The plot is barebones, furiosa on the run from Joe to take his wives to a safe "green" place. Max ends up joining them through the events that happen. Nux, is very receptive so was convinced by one of the wives that Joe is not a god, and that that's not all there is to life, and joins up with Furiosa. They find out the place is not green anymore, they plans on traveling in one direction for a long period of time without any clue as to what lies ahead. Max convinces them not to, that it's a better bet to go back to the citadel and turn that into a green place. Then they end up killing Joe and take the citadel, will probably be establishing a more stable society, help the people out there, and hope to turn that into a green place.