Yahoo! keeps their user information mainly in a DB called 'UDB'... User Database. It is a key, value store and clients are only allowed to access permitted keys. So the encrypted user password, plain-text answers to 'secret questions' (for password rests), etc. were not accessed unless a login server was compromised.

For the user's data for each property (games, mail, etc) they have their own data stores, and those would have been compromised for sure.