What is the measure of a change in an objects velocity?

Acceleration is a change in velocity, either an increase in speed or a change in direction. Acceleration measures the rate of change of an object's velocity. Average acceleration is calculated by dividing the change in velocity over the time.

In order to describe a change in an object's velocity, we have to tell how fast its speed is changing, and in what direction its speed is changing.

That's exactly the information that tells the object's acceleration.