Instagram makes it easy to share your photos. So easy, in fact, that you might share things you later regret. You don't have to delete those posts anymore, though. Starting now, Instagram has an archiving option.
Archived posts in Instagram are still visible to you, but no one else will be able to see them. To archive a post, open it, tap the overflow menu icon, and tap archive. All your archived posts are accessible from your profile page by tapping the "clock" icon at the top. Then, you can open and view the posts, and use the overflow menu to return them to your main profile page if you like.
This change is now live on Android and iOS as part of the v10.21 build. I've checked a few accounts, and it appears to be available to everyone.