1. something you know (password)
2. something you have (phone, yubikey)
3. something you are (biometrics)
With Google's two-factor, logging in requires something you know (password) and something you have (phone). The 10 passwords should be locked somewhere physically safe as a fail-safe.
Two-factor authentication protects against password leaks and brute force password attacks.[0] It now takes two security failures to access your account rather than one.
On a side note, this is why secret questions are worthless as a security measure. Backing up a password with another mental fact is still single factor authentication.
[0]: Unless the attackers were able to attain your fail-safe passwords, but unlikely given the entropy and presumably Google's security.