There were two co-executive producers who worked alongside the creator (+ may have overshadowed her a bit, but that's just my speculation) for the first half of season 1. Notice that right after that the main/Toffee plot begins and things generally get a bit less episodic.
In addition to them leaving, the creator Daron Nefcy got more control, she recognized that two storyboarders (Bisignano + Hammersley) ended up taking some of the more general episode premises they were given and turning them into completely different and better things (they're responsible for stuff like Mewberty, Blood Moon Ball, Mewnipendence Day, and Storm the Castle). So for Season 2 she promoted them to higher positions, creative director + supervising producer, and they're now on the regular writing team with her in addition to boarding.
So there's now a consistent writing team, with some others next to those 3, who have a more unified vision for the show's world and a greater focus on plot, and not just shit like "there's another exchange student and Star's so suspicious of him she thinks he's a cannibal, but he's not." Most of the boarders from Season 1 are gone (not kicked off or anything, there was just a while before they got renewed for 2 and so most had moved on) and new ones were hired, and Disney is off their backs more. For example Alfonzo and Ferguson were apparently semi-mandated by Disney, but with S2 they no longer had pressure to use them more.
Creator got more control overall and found others who felt as she did and saw more from it than "high school comedy/slice of life," more freedom to go wild with the premise and not stick to a Disney-enforced status quo.