Acceleration is a measure of how fast velocity changes. Acceleration is the change of velocity divided by the change of time. Acceleration is a vector, and therefore includes both a size and a direction. Acceleration is also a change in speed and direction, there is:

Speed (a scalar quantity) (uses no direction)

1. Distance is how far you traveled
2. Time is how long it took you to travel
3. Speed is how fast you are moving - Speed = Distance / Time

Velocity (a vector quantity) (uses a direction)

1. Displacement is how much your position has changed in what direction
2. Velocity is how quickly your position is changing and in what direction
3. Velocity = Displacement / Time

The measurement of how fast acceleration changes is called jerk.