Mad Max himself is a drifter, who, as the movie opens, is caught and enslaved by one of the warlord cultures. This culture's power flows from the fact that in a world that seems totally parched and desert-like, it controls access to a particular underground major water source and can turn the spigot on or off at will. This power makes the regular people think of the masked supreme leader as a god, and the ruling political clique as divinely mandated. The culture has an entire army of young warrior fanatics whose highest desire is to die in combat for the god figure and enter "Valhalla".
Mad Max comes to escape slavery and gets mixed up with a renegade smuggling operation in which a particular woman tries to smuggle out a half dozen young women, slave concubines of the masked water-controlling demigod. One is pregnant during the escape. The movie consists mostly of this journey, the things they go through along the way, and the dramatic chase led by personally by the masked supreme leader to recover his property (as he calls them).
The movie's limited scope is appealing (it is not something like "How our heroes save the world"). There seem to be backstories to each character and culture we see; we catch glimpses of things enough to get a vague feel for an entire world. Overall, the world we see is allusive to historical cultures and what we can surmise about prehistoric cultures.
The movie takes place in the future, though. A return to barbarism. Speaking of which, I see echoes of ISIS in Mad Max. In other words, Mad Max is a powerful vision of reality (and only a few steps removed from ISIS in Iraq and Syria, if the stories are to be believed). It is a reality stripped of all pretenses. It is a world in which scarcity bites a lot harder than it does now (scarcity still very much exists in the present day, a fact we can easily forget). The world we see in Mad Max is enormously affected by scarcity of resources following the catastrophe (which is never discussed in the movie, is probably in the distant past in the movie's universe and long out of the collective memory). I don't think we are even shocked by the barbarity of the main culture we see, because life is so hard. In such a world, we accept that this is just the way it is. Brutal.