I've heard this before, but I don't buy it. I have been using Linux for 20 years now; back in the day, and back when Ubuntu came out I was using it on my desktop (today, not so much) and I simply not believe this claim to be true. It's often repeated, but never with concrete specific examples on what was more polished and how it was more polished.
In fact I believe the opposite to be true. Back then I was using Debian on my desktop. I naturally tried Ubuntu and found out it was less polished because it contained more bugs.
Debian did none of these (at the time), it was a text installer which asked loads of questions I didn't really understand, and didn't install X or gnome or install wireless drivers by default.
Of course, I suspect the things you had to do to Debian to make Ubuntu wasn't very much -- just hide lots of installer options behind an 'advanced' option, and set a bigger set of default packages to install. But it was enough to help me get into Linux.
Sound and video playback worked out of the box for far more cases than with Debian. Networking just worked for far more network cards. X just worked the way you expected it to in many more cases. And while it certainly was buggier than Debian Stable, I don't recall it being buggier than Debian Unstable on which it was based.
Network drivers for anything other than an intel card. Still, to this day. They're not in Debian for philosophical reasons, but they're a pain-point to non-expert users.
(If someone wants cheap and simple nowadays, I recommend Chromebooks. But if they need free, as in I can re-use some of the flow of decommissioned machines from work, Ubuntu it is!)
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.