Previews of incoming text messages appear as banners or alerts on your home screen by default. This can be handy if you want to quickly decide whether you want to unlock your phone and reply to a message now or if you want to wait and reply later. But it can also be a pain if your mom or your boss catches sight of a message you'd rather they hadn't. And we all have that one friend or co-worker who thinks nothing of grabbing your phone to check out the notifications on your home screen.
Fortunately protecting your privacy (and your mom and your employment) is easy. To prevent your text messages from being on display for all to see, simply go to Settings>Notification Center>Messages, and turn off the Show Preview toggle.