Domain privacy refers to privacy concerns around the contact information that is publicly available with each domain name registration.
Some registrars offer domain privacy options, so that instead of your personal details the registrar's details will be in the whois directory. Only use domain privacy if you fully trust the provider of the service -- disputes about domain name administration or transfers may get tricky if you are not listed as the legal owner of the domain.
Different registries have different policies on what information has to be made public: e.g. .eu domains owned by private parties only have to publish an e-mail address. On the other end of the scale, .de domains require a natural person to be named with full contact information, making domain privacy services as mentioned above less practical.