The gist of it is in this part:
The government would have us remove security features and add new capabilities to the operating system, allowing a passcode to be input electronically. This would make it easier to unlock an iPhone by “brute force,” trying thousands or millions of combinations with the speed of a modern computer.
The backdoor here isn't Apple giving the NSA the passwords - it's allowing them to hook input up to a brute force system and allow unlimited tries. They still might not guess the password though.