Here is how to show time SMS text message details on an iPhone: open the conversation in Messages and swipe left on the screen, and the time each message was sent or received slides into view on the right. It isn’t obvious, but in iOS 7 and above there is a simple trick to it (like there is for most things on iPhones and iPads).
Show the time an sms text message was sent
- you just scroll to the message you want to see the information about
- and swipe with one finger from the right to the left of the screen.
The messages will slide over towards the left of the device to show the time to the right of the messages :D
Sources: apple support