SSL/SSH protects data travelling from the client to the server, SSL/SSH does not protect the persistent data stored in a database. SSL is an on-the-wire protocol.
Once an attacker gains access to your database directly (bypassing the webserver), the stored sensitive data may be exposed or misused, unless the information is protected by the database itself. Encrypting the data is a good way to mitigate this threat, but very few databases offer this type of data encryption.
The easiest way to work around this problem is to first create your own encryption package, and then use it from within your PHP scripts. PHP can assist you in this with several extensions, such as Mcrypt and Mhash, covering a wide variety of encryption algorithms. The script encrypts the data before inserting it into the database, and decrypts it when retrieving. See the references for further examples of how encryption works.
In case of truly hidden data, if its raw representation is not needed (i.e. not be displayed), hashing may also be taken into consideration. The well-known example for the hashing is storing the MD5 hash of a password in a database, instead of the password itself. See also crypt() and md5().