A Friend type relationship that would only be visible to the two people involved in the relationship.
Similar to a normal friend, making someone your Secret Friend would allow them to see Friends only posts in your LJ, and would cause their entries to appear on your Friends list. However only you and the person listed would see the link in the "Friends" and "Friend of" sections on the profile page.
This would enable you to link specific people to a secret journal without mutual friends being able to identify it's existance by tracing through Friends links.
This would eliminate a lot of the clumsy sidestepping some people do to keep from making their entire jorunal Friends Only, without making it likely that people you don't want knowing about the journal will stumble across it by acident or design.
Unless it was clearly marked, people might get confused about the difference between Friends and Secret Friends.
If Secret Friends were used extensively by many people it might lead to a general loss in connectivity among LJs, although most likely this feature would only be used by people who were already keeping their journal mostly disconected anyways.
Suggestions for Implementation:
Secret Freinds could be edited either by a seperate "Your Secret Friends" options under the "Your Settings" category, or as a checkbox that could be turned on and off next to the username in the normal "Your Friends" section.
They could be displayed either as a seperate "Secret Friends" section of your profile, or appear in the normal list of friends but with a special marker before or after their name to indicate that they are a Secret Friend that others can't see.