The coin is a commitment to the serial number. Specifically the coin is g^s * h ^ r where g and h are generators of a group where the discrete log problem is hard, s is the serial number and r is some random number known only to the minter. If you only reveal the serial number and not the randomness, there is no way to know which coin it came from. In fact for any coin c there exists an r' such that c=g^s h^r'. As such, if you only know the serial number and not random r, it is equally likely to be any coin.

The zero knowledge proof ensures no one learns r.

The serial number is never revealed. You provide a zero knowledge proof that you know a serial, and that that serial has never been spent. This proof is currently a major issue in zerocoin, because it is prohibitivly large.