The N.B. in the first bar means “nota bene”. Somewhere in the book there must be a note about the muffling sounds. It probably says that the dampening symbol applies until the next symbol for natural sounds. It probably also says that the dampening only happens in the left hand. For example, in the 26th bar, where it says “con espress”, the right hand should be played legato, though the dampening continues in the left hand.
Carl is right about the octaves in the right hand. Since the strings up there are so short, the sound dies pretty quickly anyway. Salzdo’s book Method for the Harp has an excellent study on dampening, with several techniques. For example, if there is a large gap between two notes which are to be muffled, you can use a third or fourth finger, still using the palm to dampen the sound.