To my knowledge there haven't been any outstanding innovations on the software side that haven't been available in other operating systems too, but it did so in a computer that was 10..100x cheaper than a UNIX workstation with a comparable graphical user interface.
AmigaOS was more like a stripped down UNIX (preemptive scheduling, but no memory protection/process isolation), MacOS looked like a toy in comparison to be honest, at least from the technical side.
In the later years, AmigaOS (or rather its applications) offered a glimpse into a future how applications and the underlying operating system could work together to create a professional working environment, applications didn't feel isolated, there were standards in place how UI applications can be controlled from the command line, how they can be automated through scripting, how applications can talk to each other, and how they can be extended via operating system plugins (for instance if one application added support for a new image format to the operating system, all other application dealing with images automatically gained support for this new image format too).
Basically: how can the straightforward automation from the command line brought into the domain of UI applications.
Alas, it was a glimpse into a future that would never happen.
With exception of SGI and NeXT, UNIX never had a multimedia culture.
BTW, I'm curious what you think about the question I asked in https://news.ycombinator.com/item?id=22083468
Tools like ARexx and Amiga Basic were better (IMO) than what you got on other platforms, but the OS itself was rather meh. I guess you could say it was rather interesting in the sense that it had preemptive multitasking (years before PCs and Macs would) without memory protection... but that's hardly something you'd want to carry forward to present day.