Acceleration is simply how much something changes speed over time. For example, a sports cars might accelerate from 0 to 100 kilometers per hour in 5 seconds. Meanwhile a minivan might only accelerate from 0 to 40 kilometers per hour in the same amount of time. When you ride in a car, you can feel the car speed up and slow down, but you don't feel anything if the car stays the same speed. The accelerometer in your computer only senses changes in acceleration just like you.
Perhaps a little more accurate analogy is a boat. Many laptops (Apple, IBM) only senses certain kinds of acceleration: the 1) up/down, 2) front/back and 3) side to side motions of a boat.