Apple's two-factor authentication requests a user to enter a verification code that is sent to the user's iOS device before they can use iCloud web applications. Find My iPhone is the only app that does not require a verification code in the event that a device gets lost and you can't access it.
Apple has added a 'remember this browser' toggle so that you must only enter the verification code once. Currently it seems that this feature is limited to select accounts, so we're unsure if Apple plans on rolling this out across all iCloud devices.
Apple first rolled out two-factor authentication in March of last year in the United States. It later launched the extra layer of security in Australia, Ireland, New Zealand and the U.K, Canada, France, Germany, Italy, Japan and Spain.