While you may not be able to run multiple applications simultaneously on your iPhone, you can talk on the phone and use an application at the same time.
A lot has made of the iPhone’s limitations in the multitasking department—it cannot have multiple applications running at the same time. For example, you cannot check your email while you use Skype, which is genuinely annoying. There are ways to jailbreak your iPhone and allow multiple apps to run at the same time, but proceed at your risk if you go that route.
But if you are talking to someone using the plain old phone, you can use an application like mail or Dropbox while you are still on the phone.
If you need to use the phone’s keypad during the call, there is a simple display button that allows you to easily return. This technique, however, only works when you first make a phone call. If you are using an app, you need to go back to the Home screen, make the call, and then return to the app once the call has been placed. Slightly annoying, but it still allows for more productive phone calls.