[Joe L. Ogan (OP)]

What, exactly does per second, per second mean?  In the second second, how many feet does it fall?  48 feet?

[JP]

Feet per second is speed.  We know that gravity is a force, so it causes the speed of a free falling object to increase.  We can measure the increase in feet per second every second.  This increase would be measured in units of feet per second per second.  It's also known as acceleration.

The equation to go from constant acceleration to distance moved is:
distance=1/2 x acceleration x time².

So after 1 second, the object has moved 16 feet.  After 2 seconds it's moved 64 feet.  After 3 seconds,  144 feet and so on...  In reality air resistance slows it down a bit, so this relationship doesn't hold, especially at high speeds, but its a good approximation at low speeds.