It was there in Debian (mostly) but it lacked that final bit of polish for the average user. Debian has always been very conservative as well (which is a good thing for some situations, but not necessarily for a desktop) and its documentation and guides on the terse side.
Ubuntu just clicked. It was, simply put, Linux for human beings. The user community at that time reflected this as well.
It's not just the free CDs that did it.
> But now they are abandoning Unity anyway, so it must not have been that important after all.
Unity filled a void left by the end-of-life of Gnome 2. Gnome Shell at that time was looking okay, but it had way too many bugs — and this is to be expected in a new product with new UI paradigms and libraries.
Unity was Canonical's attempt at providing a stable desktop environment that wasn't quite as revolutionary as Gnome Shell, and that could succeed Gnome 2 in stable releases of the distro. They pretty much succeeded there in my opinion. Today Gnome Shell likely is ready for mass use with all the early bugs ironed out (I hope), so Unity may not be needed as much now, but it did what it needed to do (and very well at that) for years.