You play through the 4 acts in normal mode. That is the story. Then you go in the higher difficulty and you continue from there. You keep all your gear/lvls.
The game is just played over and over again to get better gear, it's a grinding game.
So theirs no free roam or what? How does exploration work as you progress? Are their random dungeons to do or does all your loot come from story based areas?
The areas are randomly regenerated. So you play through the same act again and you'll find quests and areas you didn't get last time playing. Once you beat the story on normal you play it on the next difficult until you max your character at lev60. Then you keep playing whatever area of the game you enjoy the most, killing rarespawns and bosses to get gear. Or if you get bored of that you level up a different character. But once you beat the game on a difficult you can play whatever act you like on that difficulty.