Co-Owner status is the second-highest level of House Security, just below Owner. Since all characters on the house owner's account automatically have Owner status, Co-Owner status is usually given to characters on another account owned by the same person to allow them mostly unfettered access to various house settings. It is also sometimes given to characters of very trusted other players. A common instance of this might be a house used as a guild headquarters, vendor shop or other house where Friend house status is not enough to conduct various things. A character may only be co-owner of one house(although different characters on the same account can be co-owners to the same or different houses). The maximum number of co-owners for a single house is eight.
Beware when granting Co-Owner status! To reiterate, it allows virtually most all access to various house security commands and should only be given to very trusted fellow players when Friend level status in insufficient.