Others have already talked about trust and MC Principles and Agenda very eloquently, so I'll hit a few different aspects.
First and foremost, I love its simplicity. It takes virtually no time to pick up the rules. Tell the MC what your character is doing. It's as simple as that. If that triggers a move, the MC will tell you to roll 2D6+stat, and the narrative situation will snowball from there. For players new to RPGs or for convention games, this simplicity is freaking amazing, and means you go from zero to having a blast in virtually no time.
Second, I love that all rolls are consequential. There's no such thing as "trying again" in a PbtA game, at least not one that's run well. Oh, you missed your roll? Well, the fictional situation has changed, and now whatever you were trying to do before just ain't gonna work in the new situation. It's not that you tried to pick the lock and failed and now you get to try again, it's that as your intense concentration is causing beads of sweat to drip off the end of your nose and your fingers vainly grope to try to feel the break-point of that last tumbler, you hear a gruff voice of the guard who you could have sworn was safely off taking a piss from behind you; "Something I can help you with there, friend?" And as always, what do you do?
From a time-savings perspective, this alone lets the story proceed at a much faster clip than most other games. Where an even moderately-sized combat might grind a session in a more traditional RPG to a shuddering halt, in Apocalypse World you get to bypass all of the failed rolls, passed armor saves, or otherwise inconsequential details and get to the really important stuff - how the fallout of the battle changes the world's underlying fiction. What does it mean that we won (or lost) this fight? Whom does it effect and how? Did we make the world a better place, or did we just trade for a different kind of danger?
Third, I love Hx. I love not only the fact that all of the characters explicitly know each other, but also that both the players and the MC have concrete hooks upon which to contextualize the interactions of the PCs. Even something as simple as "one of them helped you out when it mattered" can really change the dynamics between two PCs from the very beginning of the very first session, and those choices are explicitly in the hands of the players.
Hand-in-hand with this is the idea that your character concept is not exclusively your own. When one of them says, "you cut and run when I needed you," you don't get to say, "no, I didn't." And when the guy playing the Skinner says, "your character is my lover," you don't get to say "no, I'm not." You roll with it and actively flesh out your character's back-story and relationships and find a way to make it true. This in and of itself is a HUGE departure from traditional RPG games (where PCs are often mechanically created in a vacuum) and lends itself to a much more cohesive, interesting, and dynamic set of PCs.
Finally, I love the fact that the game almost never takes away player agency over a character's actions in-game. Even if someone knocks their seduce or manipulate roll out of the park, you are never forced to take (or refrain from) any particular action. You are merely given a choice - do this and get rewarded and/or don't do it and get penalized. The choice is ultimately yours alone. Only the case of advanced go aggro deprives you of the option to suck up the damage and do whatever it was you were going to do anyway, and that's pretty hard to pull off (especially if the person you're going aggro on is trying to interfere with you). The way these agency mechanics play out in the game is absolutely brilliant.
Ultimately, AW is about telling awesome stories about hot characters. If you have a group that wants to do that, AW is one of the absolute best tools I've ever encountered in the almost 35 years I've been playing and running RPGs. And even if you don't like post-apocalyptic settings, reading the MC sections and digesting the advice therein will make you a better GM in pretty much any other game you choose to run.