The Messages app got a brand new look in iOS 7 and with that came some new features. One of them is the ability to view timestamps for every text or iMessage you send or receive. Previously you only saw sporadic timestamps but now you can see when you send and received each and every message on your iPhone or iPad.
Once you're done viewing a timestamp, just release your finger and the timestamps will again be hidden off to the side. That's all there is to it. It's not a very obvious feature at fight sight but it's definitely a welcome addition.