The definition used for average velocity in physics is change in position divided by change in time. This provides a simple and objective way to deal with all of the changes in speed and direction an object might have gone through in that time interval in order to average them out.
By velocity I assume you mean the velocity at one instant of time. This can, and for real objects, usually does change continuously over time. This "instantaneous velocity" is useful if you want to know the effects of a collision. Only the last instantaneous velocity matters for this. It is also useful in describing and determining how velocity is changing. When velocity versus time graphs are produced, the velocities graphed are assumed to be instantaneous velocities.
From such a graph acceleration can be determined as the change in velocity divided by the change in time in a given interval.
The same graph of instantaneous velocities can be used to determine how much the position of an object changed in a given time interval. In this case the procedure is much like finding an area. Treat the figure produced between the velocity line and the time axis for zero velocity as if it were a an actual area. If it's a rectangle, multiply the constant velocity by the time interval. If it's a triangle, use the triangle formula with velocity for one position variable and the time for the other.
It is possible to have instantaneous velocities that are much larger or much smaller than the average velocity within the interval over which the average velocity is calculated.
When you know there was a constant acceleration or a nearly constant acceleration, the average velocity will be the middle velocity between the initial velocity and the final velocity. E.g., if something started at zero velocity and ended at 20 m/s in 4.0 s at constant acceleration, the middle velocity is 10 m/s. Knowing this to also be the average velocity, you can find the change in position from it by using the above definition of average velocity as change in position divided by change in time. Just multiply the 10 m/s by 4.0 s to get 40 m.