Say you have two objects: a billiard ball and a feather. You drop both from the same height at the same time. You lay odds on the ball hitting the ground first -- and you're probably right, even if it's just by a split-second. However, as demonstrated by Galileo in 1589, mass does not affect gravitational pull; theoretically, all things should fall at the same rate, regardless of how heavy they are.
Back in 1971, on his last day on the moon, Apollo 15 Commander David Scott tested this theory. In one hand, he took a 1.32kg aluminium geological hammer. In his other, a 30g falcon feather, 44 times lighter than the hammer. Sure enough, when he dropped them both from the same height at the same time, they hit the ground simultaneously -- thus demonstrating Galileo's theory.
On Earth, it doesn't necessarily work this way. This is because the planet is enclosed in a bubble of gas -- the atmosphere -- which causes an effect called aerodynamic drag, particularly on objects that have a comparatively large surface area -- such as feathers or fabric. It is caused by the pressure of a medium, such as air, on a solid object. Every time you move, you are pushing against air. The denser the medium the object is moving through, the stronger the drag pressure -- which is why water is more difficult to move through than air. Aerodynamic drag is also what allows parachutes to work. The drag pressure across the surface area of the fabric is enough to slow descent to a safe speed. On the moon, there is no atmosphere -- and therefore no aerodynamic drag to slow the fall of high surface area objects. If you were to use a parachute on the moon, you'd end up looking pretty silly and possibly broken.
So why did Curiosity have a parachute? Mars, in fact, does have an atmosphere -- albeit a very thin one, made up mostly of carbon dioxide. Curiosity's parachute, about 51 feet (15.5 metres), is twice the size of a parachute that can safely drop a human on Earth -- and isn't considered safe for human missions, since a human-carrying spaceship will be a lot heavier than the Curiosity lander. To that end, NASA is currently developing what it is calling the Low-Density Supersonic Decelerator to be used in concert with a 110-foot-diameter (33.5 metres) parachute. The LDSD is a saucer-shaped inflatable designed to slow a craft while travelling at supersonic speeds through a low-density atmosphere.
And that's why Galileo was boss.