Well, they planted loads of barrels of gunpowder under the Palace of Westminster, planning to blow these up during the opening of Parliament, when the King and most of the country's other leaders would be present. After that, they hoped, England's Catholics would rise up and restore England to the true faith. I'm not sure how detailed their plans were for after that (e.g., who would be King, how much toleration the country's Protestants would have, that sort of thing), although in the end this didn't matter, because their plot was discovered after one of them wrote a letter to Lord Montague saying "Psst, your Lordship, don't tell anyone, but it might be a good idea not to attend Parliament on this date."
Basically, the POD here is that they don't get discovered, and manage to blow up the King and Parliament. What happens next? Does the hoped-for Catholic rising materialise? How successful is it? Who becomes King? What happens to the country's religious make-up? Etc.