They are used during flight planning (on the ground before takeoff) to aid in calculating fuel burn, wind correction, time en route, and other items.
60 is used in reference to the number of minutes in an hour, by placing the 60 on the airspeed in knots, on the outer ring the pilot can find how far the aircraft will travel in any given number of minutes.
This can also be done backwards to find the amount of time the aircraft will take to travel a given number of nautical miles.
Another very useful part is the conversion scale on the front outer circle, which helps convert between Fahrenheit and Celsius.
The back of the E6B is used to find ground speed and determine how much wind correction it needs.