I suspect your phone has VoiceOver turned on. If you're having trouble entering your passcode so you can turn it off in settings, you can connect your phone to iTunes and turn it off there, as described in this article: http://support.apple.com/kb/HT3577. (Just select "Neither" at step 4, click OK, then click Apply at the bottom to sync your phone.)
This would generally only happen if you had set a passcode on your phone and never subsequently synced your phone after setting it. Regardless, at this point you may have to enter the passcode on your phone with VoiceOver on.
With VoiceOver on the gestures on the phone operate differently. You first have to tap once to select an item you want to activate, then double-tap it to activate it. To enter the number 1 for example, you would first tap 1 once, then double-tap the 1 to enter it. Then continue with the other numbers in your passcode. Also, to scroll the screen, you drag or swipe the screen with three fingers.
Assuming you can enter your passcode by following this procedure, you turn off VoiceOver in settings by following these steps exactly as written:
- Press Home.
- Tap Settings. Then double-tap Settings.
- Tap General. Then double-tap General.
- Use three fingers on the screen to scroll to Accessibility.
- Tap Accessibility. Then double-tap Accessibility.
- Tap VoiceOver. Then double-tap VoiceOver.
- Tap "On" next to VoiceOver. Then double-tap "On" to turn it off.