Instagram Direct was added a while back to allow you to have conversations with other Instagram users in a more private setting. Now, Instagram is adding some features you're probably familiar with from Snapchat—you can send images and videos that self-destruct after being viewed. Regular photos can still be sent as well, though.
To send disappearing messages, simply swipe over to direct from feed and tap the blue camera icon. Then, snap a photo or record a video. When you send it, your friends in the conversation will be able to view it once, and then it's gone. This was available in Instagram previously, but it's now part of Direct. Permanent photos and videos can still be added to the conversation as well. For that, you have to use the gallery icon on the right of the text field. Of course, the direct conversations support text and reshares from the main feed, and they'll appear in the same thread with the disappearing media.
Instagram says this is just the first of several improvements it has planned for Direct in the coming year. The new disappearing messages feature is part of v10.16, which is live in the Play Store.