For any incoming SMS message, iPhone will automatically show you a preview of the message. For whatever reason (e.g. privacy), not everyone expect to have this kind of preview and its very annoying things for me too. Actually, you can avoid all this things to happen on your iPhone "Home Screen". That’s pretty easy. But it’s required to enable password lock to disable the SMS preview.

Simply go to Settings -> Passcode Lock. Enter your passcode (if you do not have one, enter a new passcode). iPhone will bring up a setting screen that allows you to turn off “Show SMS Preview“.

Once you disable SMS preview, the next time you receive any SMS, iPhone will only display a generic message (i.e. Text Message).