In light of the recent controversy, Apple issued the following statement to TechCrunch:
Some customers' devices are showing 'Connect to iTunes' after attempting an iOS update or a restore from iTunes on a Mac or PC. This reports as an Error 53 in iTunes and appears when a device fails a security test. This test was designed to check whether Touch ID works properly before the device leaves the factory.
Today, Apple released a software update that allows customers who have encountered this error message to successfully restore their device using iTunes on a Mac or PC.
We apologize for any inconvenience, this was designed to be a factory test and was not intended to affect customers. Customers who paid for an out-of-warranty replacement of their device based on this issue should contact AppleCare about a reimbursement.
Those affected received an error message telling them to update via iTunes which caused their phone to stop working. If your phone is bricked, just plug it into iTunes and the patch should get everything working again.