Galileo predicted that heavy objects and light objects would fall at the same rate. The reason for this is simple. Suppose the coin has 50 times as much mass as the feather. This means that the earth pulls 50 times as hard on the coin as it does on the feather. You might think this would cause the coin to fall faster. But because of the coin's greater mass, it's also much harder to accelerate the coin than the feather—50 times harder, in fact! The two effects exactly cancel out, and the two objects therefore fall with the same acceleration.
This rule holds true only if gravity is the only force acting on the two objects. But if the objects fall through air, then air resistance must also be taken into account.
Larger objects experience more air resistance than smaller objects. Also, the faster an object falls, the more air resistance it encounters. When the retarding force of the air just balances the downward pull of gravity, the object will no longer gain speed; it will have reached what is called its terminal velocity.
Since the feather is so much lighter than the coin, the air resistance on it very quickly builds up to equal the pull of gravity. After that, the feather gains no more speed, but just drifts slowly downward. The heavier coin, meanwhile, must fall much longer before it gathers enough speed so that air resistance will balance the gravitational force on it. The coin quickly pulls away from the feather.