It appears Instagram has begun testing support for multiple accounts on iOS. As noted by the folks at Latergramme, a number of iPhone users began noticing the new option on Thursday, which allows you to add and sign out of more than one account.
To see if you have access to the feature, make sure you have the latest version of the Instagram app, and click the Options icon in the top right-hand corner of your Profile page. Scroll to the bottom of the page, and you'll see the new 'Add Account' option.