Hi there
Unfortunately, due to security issues, Apple does not allow any apps in the App Store to record your screen. If you think about it, any app like this could potentially continue recording after you think you've shut it off and could capture personal details, like credit card numbers etc.
There are tweaks available in Cydia for jailbroken devices but personally even though I have jailbroken most of my devices in the past, I wouldn't touch those apps for exactly the same reason.
You can record your iPhone screen by connecting your device to your Mac, apparently. I don't own a Mac though *whine* so can't tell you how to do this.