I'm assuming you're reffering to the first five panels. It's series of events in Doflamingo's life, which eventually led to his life as a pirate.
It shows his meeting, or at least his first interactions with both Vergo and Trebol. Vergo shows his loyaly to Doflamingo, while Trebol must've witnessed the latter using Conquerors Haki, which most likely happened during the lynching we saw a few chapters ago. It'd explain how they managed to escape from the group of people, shooting arrows at them.
Then there's the panel with Rosinante. He probably tried to calm Doflamingo down after the lynching, but that's just a wild guess. 'Mingo wouldn't hesitate to kill the offenders if they happened to lose consciousness in front of him, but there's little to go on from just one panel.
The last two panels talk about powers, but both in different context from each other. While the panel with Doflamingo is probably reffering to the authority of the Celestial Dragon, it's likely that Trebol is talking about the revolver 'Mingo used to shoot his father. It also happens to be the same revolver he used to shoot Law, and the one to kill Rosinante, if I'm not mistaken.