An hour has sixty minutes. If you watch the minutes hand for all that time you will see it travel right around the clock from the top around the right hand side to the bottom up the left hand side to the top again, and that takes sixty minutes. When the hand is at the bottom it has taken thirty minutes, and that is half an hour.

When the hand points to the right hand side that is quarter of an hour, and you will discover that 15 minutes is one quarter of an hour, because 60 divided by 4 = 15. Dividing by 4 is cutting something into quarters. A quarter of an hour = 15 minutes. Another essentially lengthy answer which would normally be given in two words.