Instagram seems to have copied a feature security of Snapchat, which will help protect your privacy. The app will alert you if someone takes a screenshot of your temporary private messages.
Instagram's new feature is reportedly only working for news temporarily right now messages that come with the last big information of the application.
Although it is a simple copy-paste from Snapchat, the new feature is a welcome addition. The reason that comes to temporary instant messages is self-evident. Those who send such messages want to keep them private. this is also temporary.
https://twitter.com/travlim/status/801725358433148928
Of course, this will not stop someone trying to get a screenshot from another device, say a camera, but it is at least a disincentive to those who get the idea and have their mobile device only.
At this time, it's unclear whether this feature will be available to anyone, or just to iOS users, who are currently showing some testing.