Objects move because a force is acting on them, either pushing or pulling. They fall because the force of gravity pulls them towards the Earth. Forces tend to make objects accelerate, and gravity is no exception. The speed of a free-falling object, however, will depend on several factors.
A tennis-ball dropped over a high-rise building, for example, accelerates at roughly 32 feet per second. This means that each second the ball moves 32 feet per second faster than the second before. The ball is stationary at 0 feet person second. At the end of 1 second, it is traveling at 32 feet per second. At the end of 2 seconds, it moves at 64 feet per second. At the end of 3 seconds, 96 feet per second and so on. In fact, every second it travels 32 feet per second faster.
One of the important points to note about falling objects is that however heavy they are, they all fall at the same rate. The famous Italian scientist Galileo Galilei is reputed to have proven this by dropping a heavy cannonball and a light musket ball at the same time from a wall. Both objects arrived at the ground at the same time.
Air resistance is the main reason why some objects fall faster than others. A feather, for example, floats slowly downwards because it has a relatively large surface for the air to act on. A smooth, pointed bullet will fall faster than a feather because it cuts cleanly through the air. Because of the air resistance experienced by all objects as they fall, the rate of acceleration will always be slightly reduced. Only in vacuum are the figures quoted above exactly true.
The discussion above is a basic one for those interested in physics.
Galileo Galilei (Wikipedia)
Free fall (Wikipedia)
Terminal velocity (Wikipedia)
Equations for a falling body (Wikipedia)