Your iPhone can be configured to show photos of your contacts next to your conversation with that person in the Messages app. This can provide you with an additional way to recognize people as you scroll through your text messages.
The steps below will show you where to find the setting that allows that contact photo to appear at the left side of the conversation.
Adding Contact Photos to the Messages App in iOS 9
These steps were performed on an iPhone 6, in iOS 9.3.
Step 1: Tap Settings.
Step 2: Scroll down and tap Messages.
Step 3: Tap the button to the right of Show Contact Photos to turn it on. Note that you need to have a contact photo associated with a contact for that photo to appear.