The first time I noticed jerseys being nearly omnipresent and worn by what looked like the vast majority of fans may have been during the Flames run in 2004. I think Calgary has had a higher % of jersey-wearing fans than many other teams at least since then (perhaps even before, not sure).
I suspect that the onset of online retail has really advanced this trend, but there were some pop cultural elements, too, maybe.
I remember seeing Cameron (played by Alan Ruck) in 1986's classic Ferris Bueller's Day Off wearing a Gordie Howe Wings sweater which looked pretty cool. But it being a retro jersey and worn by an unusual fellow makes me think it was more meant to be seen as a whimsical thing for the character (and a way for director John Hughes, who was from Michigan, to give a nod to the Wings).
In 1994, there was the Friends episode where they went to the Rangers game and Joey wore a Rangers sweater, but none of the extras or other characters do. So I guess at that point in time it may still not have been *the* thing to do, but certainly seen as an option for 'hardcore fans'. There was also a Seinfeld character who was a hardcore Devils fan and wore a Devils sweater though this was meant to show what a lunatic this guy was.
I also know hockey sweaters for a few years in the mid to late 90s were nearly obligatory fashion items for rappers. That definitely spread the visibility of them beyond hardcore fans of hockey. I think it also made a lot of kids that generation (i.e. people now in their late 30s/40s) figure that wearing a hockey shirt can be quite fashionable and not dorky, so maybe this was actually a big part of it becoming popular.
Personally, I still don't really like it and think it looks corny.