Improvisation
Organists are often expected to improvise during a service.  In this way they can fill in gaps in the service when there would otherwise be silence, they can make a smooth link between one piece of music and the next, and they can create the right atmosphere.  In Baroque times, in the Lutheran church, organists would improvise a chorale prelude.  This was a piece of music which uses the melody of the chorale (hymn) that the congregation sang.  Bach was one of many composers who wrote many of his chorale preludes down.  In more recent times, some famous concert organists often finish an organ recital by playing an improvisation.  This might be quite a long piece with several linked movements, finishing with a fugue.  Somebody may give them the theme written on a piece of paper, so that it is quite unprepared. Charles Tournemire, Marcel Dupré, Pierre Cochereau, Pierre Pincemaille are known to be great organ improviser.