By default, anyone can view your profile on Instagram. To set your privacy so only approved followers can see your photos:
Go to your profile by tapping in the lower-right corner
Tap Edit Your Profile next to your profile picture
iPhone/iPad: Scroll down to Photos Are Private and toggle the switch to On
Android: Check the box next to Photos are Private
Once you turn on Privacy, anyone who wants to see your photos, or followers and following lists, will have to send you a follow request that will appear in your News > You feed, which you can then approve or ignore. To approve or deny a follow request, just tap on the username that appears in the request. You'll then be brought to their profile page and at the top of this page you will see an "approve" and "ignore" button.