Domain privacy is masking the information used to register your domain. When a domain is purchased from a registrar, they are required to submit information about the consumer for public record. The public database that contains this information is called WHOIS and is administered by ICANN.
Domain privacy isn't required but we recommend it. Take a look at what is included in the public registry:
One of the biggest reasons we recommend using domain privacy is to cut down on SPAM. You should never publish your email in plaintext on the internet but the WHOIS database does just that. Those that fling SPAM all over the internet will harvest your email address and start sending you junk within hours of registering your domain.
Another reason we recommend using domain privacy is junk mail by way of the Post Office. Much like those nasty SPAMMERS, unscrupulous conmen will use your information published in the WHOIS database to send you fake invoices to renew your domain. These invoices look like real invoices but at the bottom they have some fine print that says it's not an invoice but actually a solicitation. By signing the "non-invoice" and submitting payment, you agree to have your domain registration transferred to the company running the CON. Usually, their fees are higher and their support is horrible. You also run a very high chance of loosing your domain completely.