Instagram Direct lets you send messages to one or more people. To see messages you've sent with Instagram Direct, tap in the top-right corner of Feed. From there, you can manage the messages you've sent and received. When someone you follow sends you a message with Instagram Direct, you can view it by tapping in the top right of Feed.
If someone you don't follow sends you a message, it'll appear as a request in your inbox. To decline or allow the message, swipe left on the message then select Decline or Allow at the bottom of the screen. You can also tap Decline All at the bottom of the screen to ignore all requests at one time. When you allow a message request from someone, their future messages will go directly to your inbox.