Why is public key cryptography (RSA) used in sites like Google or Facebook?
[I assume you're talking about Google's web search service, and not Gmail.]

Google doesn't encrypt the web page data in storage, because it's not secret data.  Encryption is optionally used by users to securely communicate with Google, and that's different.  

Using certificate based keys and encryption assures the users that they are communicating with the Real Google and not a Fake Google that could give them false results.  It also protects the users' privacy from eavesdroppers; so if someone was searching for 'cancer' their employer or family wouldn't know.