>How is the system able to decode it then? _Something_ out there has to know how to translate that back into a readable string right?
Wrong. Password hashes are meant to be one-way and chosen specifically so that getting plaintext (readable string) from the ciphertext (hashed gibberish) is very hard. When you create an account, the plain text for your password is hashed and stored. When you want to subsequently login, the system only needs to use the exact same hashing steps and see if they produce an identical hash to the one stored.
Things are done this way specifically so that if a compromise such as the one at gawker happens, it is harder for the attacker to get people's actual passwords.
This is the primary difference between encryption, where you want to be able to recover the plaintext and hashing, where you want to make it very hard to recover the plaintext.