What do double notes mean?
In music, a double whole note (American), breve, or double note is lasting two times as long as a whole note (or semibreve). It is the second-longest note value still in use in modern music notation.
What do double notes mean piano?
It means that the C is part of the melody and also part of the harmony. If you were arranging this piece for ensemble you have two instruments on the same note.