Here is the history of this experiment. Galileo was studying the acceleration of rolling objects. His simple experiment had a slightly inclined, onto which balls of different size and weight (and material) rolled. Using a water-clock mechanism with a very precise weight balance, he calculated the time that each ball took to cover the distance.
What he discovered was fascinating, and still impresses people who watch this experiment. No matter how much an object weights, it always falls with the same acceleration rate! For example, if a feather and a steel ball fall from the same height at the same time, they will both reach ground at precisely the same time. It sounds so weird because we all know that the feather will fall much slower. That is true, but there is another force that acts to both objects: the air resistance.
If someone performs this experiment in a vacuum he will discover that both the feather and the steel ball, regardless their huge weight difference, they will both fall at the same acceleration rate. Scientists have measure this acceleration rate and found it 9.81 m/sec2 near the surface of the Earth. And since not everyone has a vacuum chamber, here is the experiment performed by Backstage Science: