that little pulldown bar at the top of the quick reply and quick compose window. If you have unread texts from that person and you pull that down, it will mark them as read.
So say you get two texts from the same person. You tap one of them to do a quick reply, type your message and send it. You still have one of the messages as unread.
Now if instead of just replying, you pull down the grey bar, after you reply, you won't have any unread messages because you marked the other message as read when you pulled the bar down.
Hope that helps.