A more thorough explanation:

A confidential marriage is a legal union between a man and a woman that is performed in some jurisdictions, such as California, where only the two parties and the officiant are present at the ceremony. This type of marriage is neither witnessed nor recorded in public records, but is recorded in nonpublic records. To obtain a confidential marriage, the parties must each be at least 18, must be of the opposite sex, and usually must have lived together for an extended period.

For example, in California, a confidential marriage allows parties who have been living as husband and wife in a jurisdiction that does not recognize informal marriages to achieve marital status without publicity. However, it does not relate back to the time when the parties started holding themselves out as a married couple and thus it can have consequences in determining the extent of marital or community property or various other rights.