Other than not having to support your weight, as mentioned ALL of your power goes toward forward movement. Walking and running are both extremely pitiful movements from an efficiency standpoint. In both you lean forward past your center of gravity and you tip forward in relation to the contact point with the ground. However, you then need to act in a way to prevent falling nose-in to the ground, and so you subsequently contact the ground whether it's walking or running (only exception being an accelerating sprinter) in front of your center of gravity, essentially braking every single step.
Not only in the horizontal plane are you wasting energy applying it both in the direction of travel and against it, but you're also going up and down constantly. You know you can burn energy running in spot, but if you're on a bike and not moving forward you burn nothing; you're just sitting on it.
On a bicycle you're never applying energy opposite to travel direction and you're never increasing or decreasing your height. Via the drive train every bit of muscle power is going to turning the crank and therefore the wheel.
I'm sure that in running the greatest energy loss is not the up/down, but rather the constant necessary braking with each step. If you think of an ice skater he glides constantly, so after a push off as long as he's balanced only wind resistance and ice friction slow him down, but simply the act of staying upright for a runner while running sucks energy.