After momentarily introducing the Peek feature in the Android version of its app in the previous beta, Instagram later pulled the feature for unknown reasons. It seems the company is now ready to roll it out again, as some users are now seeing the feature back in the latest v7.14.0 of the app. For those not aware, the Peek feature is lifted from the iOS version of the app, which makes use of the sophisticated pressure sensitive display on the iPhone 6s to let you press harder on the screen to get a 'peek' at the image without actually opening it. This lets you quickly look at the image and then release the screen for the image to pop back. The Android version uses a cruder implementation, with the user having to press and hold on the screen for a while before the image pops up and then release it for it to pop back. As mentioned before, only some users are seeing the feature even now, even if you have the latest version installed. It seems the feature is enabled server side, so you may have to wait a while even if you get the latest update before you can start using it. Source ...
Source: http://www.gsmarena.com/instagram_brings_back_the_peek_feature_to_its_android_app-news-15817.php