Problem number one is that people are saying that the gyroscope is the same as an accelerator but more accurate. This is dead wrong. They measure completely different things. The accelerometer measures acceleration and because we are in a gravity field, it can determine orientation. The gryroscope measures angular acceleration and can therefore determine rotation. Can you get one or the other by integrating the accelerometer's output or taking the derivative of the gyroscope's output? Somewhat. But it will never be as accurate as simply using the correct device. They both go hand in hand. Combine a 3 axis accelerometer with a 3 axis gryroscope and you get the so called 6 axis motion detection seen in stuff like the PS3 controllers. And no, a compass will give you neither.
The wikipedia pages on these two devices are good. For the people who actually want to learn, what don't you get?