"Private" is one of the variables you can set. When private is non-zero, games you play cannot be observed by other users. If private is 0, other users will be able to observe your game - unless your opponent has private non-zero. A private game is designated in "games" and "history" displays by the letter "p". Also, if a game is private, the eco category is not displayed in the history table.
See also: eco, games, history, observe, variables