It is very much Dirty World with superpowers. It's pretty much the exact character mechanics with new names and superpowers tacked on.
So everything is paired. Strategies are the equivalent of stats. Each Strategy can be paired with four Tactics (like skills). There are three of these groups, each roughly addressing Mental, Physical, and Social actions. Certain powers allow you to pair Strategies from different areas with Tactics from another area.
Every Strategy and Tactic has an opposite. So if Insightful is the Virtuous Strategy, Deceit is the Sinister. A slide means one dot from the Sinister side moves to the Virtuous side (Deceit to Insightful, in this example) or vice versa. Tactics work the same way.
When you roll, you use the dice pool of your combined Strategy and Tactic for that option. The tricky part about BA is that these are expressed in moralistic terms, but the only person that really needs to know what dice pool to use is the GM. So, to punch somebody stronger than you, roll Open (Virtuous) Courage (Virtuous Tactic). To hit an unarmed person, roll Open (still Virtuous because he aren't trying to hide your actions, at least) Cruelty (Sinister Tactic because you're being an asshole). Shooting a puppy would be Sly (Sinister, because the gun is doing the dirty work for you) Cruelty (again, for being a bastard).
You roll your pool. There's also possible bonuses for weapons (in physical actions), surprise (combat and mental actions), and knowing secrets (social interactions). Bonuses are between 1-3 dice, and the player gets to choose when to use them. They can use them for extra dice BEFORE the roll, making a 5d pool into an 8d pool. Or they can roll their unaltered pool and take the bonus as extra width. To return to the previous example, the 5d pool with a +3 bonus rolls 2x3, but that becomes 5x3.
Width is important because it determines speed and damage (in ORE and real life, speed kills). This is where sliding and obliterating comes in. For rolls of 2 or 3 width, the targeted tactic slide to its opposite. So if I guilt trip your character with Devious Nurture (persuade with decency), I declare an attack on your Corruption. If I get a 3x4 and you get nothing to defend, your Corruption die SLIDES over to Nurture. I've made you a better person, or at least made it harder for you to be a shitty person.
For rolls of 4 width, serious damage starts. At 4 width, I don't slide the dot; I remove it. You don't reallocate your character's dice pool, you lose one from it permanently and have to perform sin/repentance to level it back up. If you are already down to zero in a Tactic, I remove a die from the Strategy attached to it and it has negative effects on all four Tactics linked to it.
At 5 width, I skip the targeted Tactic altogether and remove a Strategy attached to it. It doesn't matter if there's Tactics left in the target, the damage jumps up and does damage to every other Tactic as well by attacking the attached Strategy.
To provide an example from the game, David's Grackle Cannon was a great weapon. The birds it fired attacked Generosity by stealing money and things with their beaks. Now, what David would do, he'd forgo the weapon bonus to hit and use it for damage. He'd get this paltry 2x5 set or something, but then he'd boost it with his bonus dice. A 5x5 hits the attached Virtuous Strategy (Patient) and wipes out the dice. This would take the target's Patient down to zero really quick, and a character with no Patient left either goes completely berserk or runs away. Essentially, his plan for every fight was to annoy his enemies so much with birds that they made stupid choices.
Does that make sense? It's easier to get the weird moralistic expressions of every action if you're already familiar with ORE, I'll admit, but once you play a few sessions its easy to get the hang of. And it's a fun system. There are multiple solutions for ever problem. You can talk down the big bad or sucker punch your allies. It makes for unpredictable, fun roleplaying.