The Amiga was a milestone in so many ways, it introduced the concept of custom chips, where the CPU subbed out the previously time consuming tasks to co-processors instead of being relied upon to do everything.
It's games machine roots meant it brought state of the art graphics and sound to the user. Instead of the tinny whistles of the AY38912, we had deep bassy synths and amplitude modulation of samples - again independant of the CPU. The Amiga could scroll smoothly, could move sprites around smoothly and display the end result in an unprecedented array of colour.
The Amiga was a "do anything" machine, way before we all started using our hitherto office based PCs for playing Doom etc.
Mulitmedia presentations, cheaper movie special effects, the demo scene and 3d graphics manipulation are all legacies of our favorite platform.