Capturing a video of whatever is on the screen of your iPhone, iPod touch or iPad in real-time normally requires a jailbroken device and one of useful Cydia apps such as ScreenRecorder or Display Recorder by Ryan Petrich.
Official App Store solutions are unfortunately far and few between. And even when such an app does slip past the App Store approval team, it's only briefly.
Tapping iOS video recording APIs, xRec by developer Akın Öğünç lets you easily capture contents of your iDevice's screen, without having to jailbreak or cheat by hooking up your device to a computer to use a desktop screen capture software instead...