Instagram has added a new activity status feature in its iOS and Android app. Considering there isnt an official announcement from the company, its likely the feature is still being tested and not available for everyone. However, it does seem to be available for most users right now.
With this feature, enabled by default in the app settings, you can go into your direct message inbox and see the activity status of the people you have messaged below their name. This appears for people you follow or have previously messaged. The status ranges from Active a certain time ago or a very specific Active now if the user is browsing Instagram at that very moment.
If this sounds like a bit much to you, then the app does give you the option to disable the feature. When you disable Show Activity Status, you stop seeing status for other people they stop seeing it for you.
There were reports of Instagram spinning off its direct message feature into a separate app and this might be an effort towards that.