And your social graph. You implicitly give it information about all your interactions and connections - and allow it to record even interactions you aren't aware of (like other FB users looking you up or checking your profile without interacting with you in ways you find out about). You're also opting in to web-wide surveillance, where FB track you individually across every webpage with Facebook social widget on it (unless you take steps to manage your browser's FB login status - and most likely even if you do log out whenever you're done with FB by using "industry standard" ad network browser fingerprinting...)
I’ve had friends have to submit government ID to prove that they were using their real name.
The problem is, that after you sign up and enter only your e-mail address, Facebook will fill in all the blanks for you, without needing any interaction from your side...
edit: cleaning up the grammar
I've stripped most of my personal information off Facebook and now just use it as a messaging app and a "find me by name" sort of internet yellow pages thing.