When you open your profile on Instagram you’ll see a new option along side the discover people option. Click on that it will take you to the page where all your archived photos and videos will be saved.
To archive a post just click on the three-dot menu option located on the right side of the post and click the ‘archive’ option which is located on the top of the pop menu. Now your post has been saved to archive folder and is hidden from your profile.
To unarchive it just click on the post menu option and click on ‘show on profile’ and it will appear again on your profile again.