The right password can be obtained by either knowing it, or by guessing it.
As an additional security measure, the software shipped with the phone prevents brute force attacks by wiping the device after a given number of failed attempts.
Apple has been asked to modify the software so that it won't wipe the phone, thus allowing the authorities to try many passwords.
If anybody could circumvent this additional security measure, actual security would be lower. The authorities are not asking Apple to ship this change to all users: they only want to install it on the device in their possession.
However, Apple is concerned that once they provide the authorities such a modified software, it could be leaked and thus be used by third parties to breach the security of any Apple device.
It should be noted that currently all data encrypted for example on your laptop's hard drive is already subject to this kind of brute force attacks. It's a well known fact that authorities or malicious users can already attempt brute force attacks on encrypted data if they can access the data on a passive device such as a hard-drive.
It's important to understand that Apple (at least not in this case) is not being asked to implement a backdoor in the encryption software. It's also important to understand that even if Apple was forced to install a backdoor, it would affect only the ability to access future data and not help the investigation of the San Bernardino case.
This very request by the Authorities suggests that Apple does not currently install any backdoor on stock phones.
However there is a logical possibility that the Authorities are either not aware of any such backdoor or in the worst case they are publicly requesting this feature just to hide the real reason of a possible future success at decrypting the phone: they can claim that Apple didn't have any backdoor, and they were just lucky at bruteforcing the device; in fact Apple wasn't even cooperating with them at relaxing the brute force prevention limit, so they could claim they did it in house.
(I'm personally not inclined to believe in such improbably well coordinated smoke and mirrors strategies, but they are a logical possibility nevertheless).