Since acceleration is the change in velocity over time, we need to find both the difference in velocity as well as the duration of time.
The change in time in the formula is so that we can obtain the duration of time in which the object accelerate.
Let's say the question wants you to find the acceleration of a car from t=2s to t=5s. The time (denominator of formula) cannot be 2 or 5 since that is not the whole duration of the acceleration we are trying to find. So to find the duration, we take 5-2= 3s, which is essentially the change in time.
