Speed is a rate, a ratio between two different quantities.
For example if a soccer player kicks a soccer ball on the ground 50 yards in two seconds the ball would be traveling 25 yards per second. This would be the average speed of the ball. At some point the ball may have been going slower than 25 yards per second, but that is the average speed. This is the difference between the final velocity and the initial velocity. Since speed is measured in meters per second, acceleration is measured in meters per second per second or meters per second squared.