On the iPhone 6/6 Plus and 6s/6s Plus, with iOS 9, the Messages app—the one you use not only for sending SMS/MMs texts, but also iMessage messages—got a new feature. Pics from your iPhone Contacts list show up next to the person who sent the message. Very nice—unless you hate it. iOS 9.1 added an option in Settings > Messages to turn off Show Contact Photos.
Not seeing that option? Check Setting > Display & Brightness > View and if set to Zoomed toggle to Standard.