Wow, thats a hard one to answer ! Where do I start ?
Well, Amiga is a computer we had/have and it can be found in various models from small console sized ones up to desktop computers.
Amiga is also the operating system that we love to use, that we love to fiddle with, and hack around with to make it do what we want.
Amiga's are still in use all around the world, and can be emulated on many other computers to allow others of us to keep using the OS.
Amiga OS has never been open source and is not likely to become so, since OS4 is very close to release.
Amiga is what you make of it, and good fun while you are doing it as well.
Does that cover it ?