What is the meaning of M. M. = 72 printed over a piece of music?

The M stands for "metronome," the other for the name of its inventor, Maelzl. The figures indicate the number of beats a minute and the note shows what each beat represents—in this case a quarter note. The whole annotation says that the average speed of the piece should admit of seventy-two quarter notes being played in a minute. I advise you, however, rather to consult the state of your technique and your own feeling for what is musically right in deciding upon the speed of the piece.