At the start of each Job, a player character gains at least 1 Flashback. They receive an additional Flashback per Job for each Breakthrough.
A Flashback is a resource that represents some sort of preparation they've made for the Job they're currently executing. As a player, you can activate the Flashback at any point during the Job, no actual preparation is required.
When you activate a Flashback, you make a suggestion to the Conductor on how to overcome a particular challenge you are facing on the Job. 1 Flashback is then spent. You allude to some preparation your character would have made to tackle a situation exactly like this. You and the Conductor then play out the Flashback, perhaps with some challenges involved, depending on how you much you demand from the Conductor. After the Flashback plays out, you return to the current story and are then allowed to use whatever information you've learned or resources you've gained retroactively.
The Player Bertrand controls the character Fucetti. Fucetti and his party get caught stealing some priceless artifacts from the national museum. There's only a single security guard who spots them. Bertrand decides to spend his Flashback to tell the Conductor that Fucetti befriended the security guard a couple of weeks before.
The Conductor accepts, and they act out a scene where Fucetti and the security guard hang out at a strip club while the security guard complains about his boring job. Fucetti buys him drinks and shows empathy.
Now, the Conductor thinks this is a good idea, but that doesn't get the party completely off the hook. The security guard sees Fucetti and tells him: "Look, I don't get paid enough to stop you guys, but I do need to report this. I can stall for a few minutes but at some point, I'll have to press the alarm." And thus Bertrand won the party some precious time.
The elevator grinds to a halt and your party is stuck inside as the power turns off. The strong guy tries and fails to open the doors, and the hatches seem sealed shut. The player Marco controls the character Nancy. Marco uses a Flashback to tell the Conductor that Nancy went out shopping in the black market specifically to find some sort of laser cutter.
The Conductor accepts but tells Marco that with the loot from his previous Jobs, he wouldn't have enough money for that type of high-grade gear. Luckily, Nancy is a very social character, so Marco rolls a bunch of successful Charm checks to bargain the price down. The Conductor accepts, and Nancy uses her laser cutter to cut through the doors and free the party.