The power source on a bicycle is the rotation of the pedals as they are pushed by the feet of the rider. As the pedals rotate, the chain wheel also rotates at the same speed as the pedals since it is attached to the same axle as the pedals. The chain on the bicycle is moved because the links of the chain are meshed with the "teeth" on the chain wheel.
As the chain is rotated by the chain wheel, that movement causes the chain wheel attached to the rear tire axle to also rotate. The chain passes over one or more derailleur gears as it moves around its path between the two chain wheels. These gears increase or decrease the speed at which the rear chain wheel causes the rear axle (and therefore the attached rear tire) to rotate. This is how the bicycle rider can adjust the speed and pressure that must be exerted to make the bike move. If the chain wheel attached to the pedals didn't move, the bike would move only in response to gravity as it rolled down a hill.