Notaries are private parties, who are licensed by the State of California to formally witness signatures. For a small fee, a notary will place a stamp upon documents. This stamp provides a higher level of evidence that a document was, in fact, signed by the party who has purported to sign it.
In California, notaries are not attorneys, and they are not qualified to give legal advice. This can be confusing, for those accustomed to doing business in Mexico. In Mexico, notaries are more highly trained, and perform a wider variety of functions than in California.
The California Secretary of State regulates notaries. The laws governing notaries are set out in California Government Code Sections 8200 and subsequent statutes.
A real estate contract does not have to be notarized. Likewise, offers, counter-offers and acceptances need not be notarized. You can, if you like, have any of these documents notarized, but California law does not require it. Many real estate documents have to be notarized. Any document, which will be recorded, has to be notarized.