I am trying to inject some clarity into this discussion. A Google search will show many options, unfortunately they are mostly plain wrong and will end up wasting your time so here’s the facts.
1. Error 53 means “Hardware error”
2. Error 53 whilst upgrading a phone to any iOS except 9 is a recoverable hardware error. It’s probably, though not certainly down to a faulty cable.
3. If your phone is under warranty, take it back to an Apple Store immediately. Insist they replace it under warranty
4. If you are upgrading to iOS 9 on a iPhone 6 and you have had either the screen or the home button replaced by a third-party repair shop, you’re fucked. It’s bricked. Even Apple can’t repair it though they may offer you a reduced price on a new phone.
So. It’s important (and hopefully you’re here because you’re curious and not because you’re looking at Error 53 ) that 1. if you have your screen repaired keep the old home button and cable, 2. if you have problems during warranty, go straight to Apple. 3. If you had your iPhone repaired at a third party don’t upgrade to iOS 9 4. Don’t fall prey to the vultures on the internet.