Not that it was (is) blazing fast and technologically advanced in comparison to other models but the fact that it seems to have come from a whole another plane of technology.
Surely it helps to have multiple special-purpose chips onboard as it helps to have dense battery pack worth of 500km baked into the chassis. But that's not the thing.
What a 32-bit pre-emptively multitasking operating system with modern library stacks and system services for building user interfaces and applications was to old machines where you poked memory addresses directly to draw something on the screen is quite akin to what an internet-connected fully electrically powered and from-the-ground-up architected smart&mobile device-on-wheels is to clunkers primarily designed to host an oily, fire-burning engine and an appropriate steel drivetrain, with a passenger cabin retrofitted wherever there's space left from the mechanical components.
You could write high-level code and put that space ship spinning on the screen, and still have it rotate more smoothly than in any of the machines from preceding era—where no operating system or user interface was messing in the way. That was like having the cake and eating it too. And yet you could switch to "insane mode" by suspending the operating system and commanding the special chips directly, and do things people couldn't even imagine on 8-bit machines (and for the most part, on 16-bit machines too).
Amiga had elements so modern that it almost lasted till the end of the 90's, except for cpu power and marketshare. Considering it was born in the early 80's when 8-bit cpus could beep and produce blocks of color on the screen and died (for all practical purposes) in the internet era, that's one long stretch of time where it made the difference.