Suppose you drive a distance of 500 miles in 9 hours, taking a stop for lunch. What was your average speed?
Just to look good to the crowd, you speed up at the last minute and cross the finish line at 60 mph. What was your final speed? (Yes, that really is as trivial a question as it looks!)
Probably you are looking at a problem where you are dropping something. Let's say you drop a ball and it take 2 seconds to hit the ground. Since the acceleration is 9.8 m/s2, in those two seconds its speed increases from 0 by 9.8(2)= 19.6 so its final speed is 19.6 m/s.
For the simple case of "constant acceleration", the average speed is just the arithmetic average of the initial and final speeds: here (0+ 19.6)/2= 9.8 m/s.