I'm trying to think of the most unique new aspect that was introduced, i.e. not a simple extension of an existing feature. Battling/trading between games was available in the original games, so Wi-fi wasn't that stunning. Physical/special was overdue, although I'll admit I hadn't really thought about it before it was done (probably because I didn't really know how it worked back then) so it was something of a nice surprise.
Weather/daylight was a pretty good addition (seasons less so), and come a close third. The new types come second in my list, although I don't think they're quite as revolutionary given they showed up in only the second generation, so there wasn't much to revolutionise - the same goes for breeding.
My top spot goes to abilities. They were completely different to any other feature, and can have profound effects on the game. The expansions on this feature to dual abilities and Dream World exclusive ones are both good.
The follow feature was just another gimmick in a game that could only be supported by extras - Gold/Silver didn't have much to them, so the remakes had to throw as much as possible into them to keep them interesting. I never cared for the follow feature, and certainly don't miss it, and I'm surprised by how many people claim it's the best thing ever. Also, it showed up on Yellow, a time when there was almost nothing to revolutionise in the first place! So no, that feature is in no way revolutionary.