The iPhone keeps a record of all sent and received text messages until you delete them. You can delete all sent and received messages associated with a specific number to free up disk space or just to remove texts from a number that you won't ever need to check again. After sent and received messages associated with a specific number have been deleted, you will not be able to recover those messages.
Tap the "Messages" app on your iPhone home screen.
Tap the "Edit" button in the top-left corner of the screen. Alternatively, sweep left or right over the phone number in the message history.
Tap the red "Delete" button that appears on the right side of the message. All conversations associated with that phone number are now permanently deleted from the iPhone's text messaging history.