By default, iPhone displays a preview of new messages when iPhone is locked or you are using another application. You can turn this preview on or off in Settings. You can also enable alerts for text messages.
In Settings, choose Messages and tap Show Preview.
In Settings, choose Messages and tap Repeat Alert. If you don’t respond to the first preview of a new message, the preview will be displayed twice more.
In Settings, choose Sounds, then tap New Text Message. Tap the alert sound you want, or None if you don’t want an audible alert.
IMPORTANT: If the Ring/Silent switch is off, text alerts won’t sound.