Try this one for a lay explanation:
Vy is based on how much power you have in excess of the amount of power you have to maintain straight and level flight. Think about flying straight and level at 70 kts in a 172. Very little power is needed. Increase power, maintaining the 70 kts, and you climb. More power, higher rate of climb. Vy is the airspeed at which the difference between power available and power required for straight and level flight is the greatest. As you increase in altitude, there is less power available, so the airspeed at which the difference is the greatest goes down.
On the other hand, Vx is based on available thrust. Vx is the airspeed in which the greatest amount of thrust is available. An airplane with virtually unlimited thrust could fly straight up and the distance it can climb within a set horizontal distance be "infinite" (very loosely speaking). Think of our cartoon view of a rocket ship - straight up to outer space with no horizontal movement at all - forward airspeed is zero. (Of course, we don't fly airplanes that go straight up, but it helps visualize the concept.) As altitude increases, the amount of thrust also decreases - less power available to produce the thrust, more propeller "slippage" as air density gets thinner, etc. So, the airplane can't go straight up any more. In order to climb, we now have to lower the nose. Which in turn means an increase in airspeed.