When you register a domain you're required by Internet Corporation for Assigned Names and Numbers (ICANN) to enter correct contact information including address and e-mail. The information is publically accessed through the WHOIS database. Not only your privacy information is exposed, but this is a potential risk to receive unsolicited e-mail messages.
The WHOIS Privacy ID hides the original information about you, by masking it under the name of another company responsible for the legal matters. You're still the onwer of the web site, and the domain name is under the ICANN rules, although the information about you cannot be accessed without a permission.
Note that it may not be always a good idea to hide your contact information, especially when you are a merchant and you want to keep confidence and transperancy with your customers.