Performing music from memory
Most Classical musicians will agree that it is good to play from memory when performing as a soloist.  It means that the player understands the music really well, and he is able to concentrate completely on the way he plays the music (the interpretation).  In some music competitions the competitors are expected to play from memory.  A pianist playing a recital will usually play everything from memory.  It is particularly important for singers who are performing songs (Lieder) to sing without music because they can then communicate directly with the audience using the expression on their faces.  Some conductors conduct from memory.  If they do, they ought to know every single note for every single instrument from memory. There are some conductors who have such amazing memories that they can do this.