Season 1 was marketed as the Bart Simpson = crazy troublemaker bonanza. The show focused on his being a bad influence and, in the US at least, there was much chatter over Bart Simpson being the worst thing to happen to god-fearing Americans. None of it was truly funny. I mean, for a ~9? year-old, "Don't have a Cow, man!" seemed funny enough to base your show, but whatever....it was a horrible season. Oh, I forgot that sideshow Bob first appeared in season 1. That was a decent episode. It sold shit-loads of merch, though. Hence the phenomenon.
I recall that it was season 2 or 3, when the slot was moved to Thursday night opposite the slot of Cosby, the long-standing titan of sitcoms. Cosby was not happy with this, especially as he agreed that Bart Simpson was the antithesis of what he was doing with his show (which is very much true). Dad didn't want us watching anymore (mainly because Cosby was much preferred--we all enjoyed both, anyway), but Simpsons eventually won out because those were the years where the writers realized that the show should be about Homer.
I recall season 2 being good--I think the introduction of Uncle Herb midway through? The first truly good episode, that I recall. I believe season 3 opened with the return of Uncle Herb--also great, and was, of course, the season of the legendary baseball episode. I also recall it being the first Treehouse of Horror season? maybe that was season 2.
The real kicker for the golden age of the Simpsons, though?
Phil Hartman. The show lost its soul when he was tragically murdered.