The traditional multitasking example is playing music while web browsing. On the iPhone, this can only be done with the built in player, not any other music apps such as Spotify. There's many other examples too, such as writing an email and switching back and forth to the web browser to check some facts for your email. Or want to be on Windows Live Messenger (aka MSN Live) on your phone while playing a game? Not on your iPhone. Want to run a VoIP client (e.g. Skype) while playing a game? Not on your iPhone. Want to be on Windows Live Messenger, AIM, Skype and more, while gaming, browsing and emailing? On your iPhone, pick any one. On Android, well, performance would be stretched but you can have them running all at once.
Right now on this PC, I have Firefox, Pro Evo Soccer and NuSphere PHPed (programming application) running, backed up by instant messengers, Steam gaming software and loads more - that's multitasking.
Other advantages are that it's far more customisable, with things like desktop widgets.
With Android, you can choose your handset. Want a physical keyboard? Fine. Want a small device? Fine. Want a massive 4.3" device? Fine (soon). Want an OLED display? Fine. Want a high end device? Fine. Want a low end device? Fine. iPhone - want a 3.5" HVGA screen with only a soft keyboard? Fine. Want *any* other configuration? Uh ... no.
Speaking of OLED, sit an iPhone next to a Desire. The iPhone's screen will look bland and ill. Plus the viewing angles are vastly better.
The big advantage is that Android doesn't have Uncle Steve telling me what I can and can not do with it. This is a hard point to get across to non-techies but it's a very, very big deal and I believe in time, it will relegate the iPhone to the same position as Mac computers - fine for the market fraction for whom the limitations aren't an issue, but ultimately marginalised.
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You say you've never used an iPhone. I bet they've never used a Desire. Quite a lot of iPhone users (far from all, let's not generalise) are iCult members, they're blinkered to seeing Apple as the best, in this case it's like arguing with a Creationist - just let them wallow in their ignorance. The only thing the iPhone has over Android is the app store size and I believe that will change.
iPhone 4 will add multitasking, although it remains to be seen how well. It may be a half-job where apps can only run partial services in the background (which Android has, as well as fuller multitasking, as does Symbian, WebOS and others). The next iPhone looks a lot nicer than the current iPhones, which IMHO it looks dated. Most interesting will be the screen, which, allegedly, is 4 times the resolution of current iPhones and higher even than the Desire (which has about 2.5x the number of pixels than the 3GS). If that's true, it will be very sharp. If it's also OLED, I will be jealous of that. However, I still wouldn't swap my Desire for one and the way these things go, an Android device will soon be released that matches it, and then one that overtakes it.
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I've rambled between the Desire, and Android in general, but I hope my points come across.
With the iPhone 4, Apple are playing catch-up with Android in technical terms (sadly, Android is way behind Apple in mindshare terms). If the iPhone 4 does surpass the Desire or Evo, in a couple of months an Android phone will surpass the iPhone 4.
EDIT: Actually,
Celox sums it up very accurately and concisely.