I hear this word all the time. Are people just talking about widgets on the home screen and 3rd party apps? I understand those. But is that really why people love android so much? Those two little things.
Please list everything else under the "customization" criteria that you can. I need to know if it's just rhetoric or if you can customize anything and everything to be or do however you want it.
Launcher: This is the homescreen/appdraw apk (app executable), and if you download a different one you can change the look of your homescreen, appdrawer and everything in it, down to animations.
Widgets, well we all know what they are.
ROM: You can change (only if you have root permissions, aka jailbreak, which is legal on phones) the ENTIRE look of the OS, add fetures, take away features etc. But this is more advanced stuff.
Kernel and Overclocking: you can change the kernel, which allows you to overclock (which isn't very smart) or make your phone run better, have better battery performance etc. Also more advanced.
Lock screen customization: This is like the laucher, but allows you to change your lock screen, you can add widgets, change clocks, have completely different looks.
Status Bar (it has many names, but for Apple peeps it is Notifications Center): Now on android (stock, no touchwiz etc) this looks very good already, but you can change that aswell, which is like the launcher thing also.
LED Nofications: On some android smartphones they have a LED light for notifications, to tell you if you have a text or if your battery is finished charging, you can change the color of this, the brightness (I believe), and the reason it does it.
Keyboard: You can basically customize the keyboard to suit you.
The thing about android is it is open source (AOSP) which means, you can change ANYTHING, on some phones you can dual boot WebOS on it, if you are a dev then you have every bit of code that Google has written at your disposal, so customization is endless on android.