After a limited rollout nearly a year ago, Instagram has rolled out two-factor authentication to all users. The new security feature can be enabled through settings and once it is done, it will require that you authenticate not only with your password but with a SMS code sent to you phone. This will only be required if you log out of the app and not every time you use it (assuming you keep yourself logged in).
Two-Factor authentication is something I highly encourage readers to enable on all their accounts, especially social networks. It significantly cuts down on your risk of your account being compromised. Yes it is a pain to have to deal with but it is better than the alternative.