A false flag operation is when you do something bad with the express purpose of making it look like someone else did it. For example, lets say you want person A and person B to fight. You decide to slash the tires on person B's car, and let yourself get caught on film while dressed like person A. Person B is going to assume person A did it, and since he has "proof" he's much more likely to go for immediate retribution rather than try and think it through. I mean, after all, person A is the only person who can refute it and, to person B, he's got the motive to lie. Heck, you could even cut out the middle man and just say Person B slashed his own tires in such a way that makes A look guilty, so he can do something to him while being "justified".
It tends to come up a lot with conspiracy theorists using the logic that "This group would benefit in some way from a tragedy happening to them, ergo, it's possible they manufactured the tragedy themselves". Like people who say the 9/11 attacks were done by the U.S. so we could attack Afghanistan/Iraq, or the classic "burnt down their house for the insurance money". It mostly doesn't make sense because effective false flag operations are SUPER difficult to pull off under any amount of scrutiny and the consequences of getting caught tend to outweigh the benefits (unless you just don't care, of course). That doesn't stop people from seeing them everywhere though.
It's amazing what a little context can do.