Counterpoint
A different way of playing it would be to start the tune with the right hand.  Then, in the second bar (measure), as the fifth note is played, the left hand starts to play the tune an octave lower.  This works well for a time, but in the fifth bar (on the word “Up” in the right hand part) it starts to get dissonant (sounding unpleasant), so changes need to made to the left hand to make it sound nicer.  This way of writing with a particular number of parts (in this case: two) is called "contrapuntal music".