How does building from source make it stable?
Right, it doesn't. I dunno why I typed that really. I was in a rush. But now I'm not, so I'll do Gentoo a bit of better justice.

What really makes it stable is the way you can choose which sources get downloaded and compiled. By default, it's the packages marked as stable by all the Gentoo devs who work on testing and fixing all the packages in Gentoo's tree. Granted, these packages aren't always the newest, which is likely the case for a binary distro anyway.
However, the vast majority of package sets also have newer sources marked as unstable, either because it has a few bugs that need fixing, or hasn't been fully tested and verified for stability yet. You can freely unmask these unstable packages and use them. But if you keep the stable package set, you end up with a bug-free system nearly all of the time.
The package tree (called Portage) is kept in sync via rsync; it's updated every day, all the time, and Gentoo provides you with some nice commands to sync and update your system, or install/uninstall whichever packages. You can also check for packages that are redundant (dependancies that are no longer needed) and also fix broken reverse dependencies. That way you system doesn't get b0rked if you like to test lots of new software.

It is remarkably easy to switch between bleeding-edge and stable, for any number of packages. You just keep a list of the ones you want to use in their unstable forms.
You can also add one or more of the many "overlays" which people make. This so you can add an unsupported 3rd party set of packages over the top of the main tree. This way, for eg. you can fetch and build a brand new package from SVN, keep the package in sync with SVN, or cleanly remove it.
It also has a config file protection system, so if an updated package comes with a new syntax in its config file, your old one won't get zapped. It will alert you, and you can choose which config file to keep, or do an interactive merge based on the diffs.
Finally, the best part. USE flags.
With Gentoo, you can easily keep the number of dependencies that are pulled in by certain apps to a minimum. Since everything gets compiled from sources, you get to choose what gets compiled in.
Say for e.g. you wanted to install a music player. By default, it might be compiled with aRTs, ESD, OSS and so on. As a result, it would depend on those other apps, and they'd get pulled in and compiled. aRTs might in turn depend on all sorts of KDE libraries, so if you wanted to keep a GNOME-only system, you might get half of KDE pulled in just because you installed a music player.
In Gentoo you can set so called USE flags. Every package is marked with these flags which are used globally.
E.g, I want to keep a totally KDE-free system. I don't want any KDE or QT libraries installed:
-kde -qt -arts - any apps which make use of KDE, QT or aRTs are either compiled without support for them (saving time/space/packages being pulled in) or not compiled at all (maybe because they really need them to run).
+alsa -oss +mp3 - any audio-related apps I compile that make use of these flags will be ALSA enabled, won't be compiled with old-style OSS driver support, and they will compile in support for playing MP3s.
In this way, you save on the amount of bloat/useless packages being installed, and you keep your apps lean and mean.
The main killer app of Gentoo just has to be its package system. I am not saying Gentoo is better than any other distro, because frankly, I've only ever used Slackware and Mandrake before Gentoo. But it's just my distro of choice; all I can say is try it.

Have a look at
http://gentoo-portage.com, which is a website-ified version of the package tree; it might give you an idea of how it works.