In Direct, under a person's name, you'll now see when they last opened up the Instagram app with a message like "Active Now" or "Active 2h ago." This is similar to how other apps like Facebook Messenger work, letting people you've previously interacted with know when you're online.
The activity indicator is enabled by default and appears to be limited to people you've chatted with via direct messages. According to The Verge, your online status is visible to people you follow or have previously DM'd, with the info not accessible to general followers.
If you would prefer not to have your online status available on Instagram, you can turn it off in the Settings app under a new option called "Show Activity Status." If you disable the feature, no one will be able to see when you're online, but you also won't be able to see the online status of your friends.
The activity indicator appears to be a feature that's been quietly rolled out to all iOS and Android users.
In related news, Instagram is currently testing another new feature called "Type," which is designed to allow users to share text-only posts via Instagram Stories. The text-only feature appears to be similar in design to the Facebook feature that lets you accentuate text-only posts with large fonts and colorful backgrounds, as seen in this video shared by The Next Web.
Type is not available to all users at this time, but those who have access can use it when sharing a story. The Type button is available next to other Instagram Stories camera options like Boomerang and Rewind, with several fonts and backgrounds available.