Delivery time is the total time the ball is in the player’s hand from initial movement to the release of the ball.
It is important for a pitcher to keep her delivery the same across different pitch types. This makes it harder for batters to pick up on different pitches being thrown.
For position players, reducing time to deliver the ball to the base reduces the distance a baserunner travels while the fielder has the ball in her hands.
Real Life Example:
If a pitcher has a different movement between say, his fastball and curveball deliveries, it may be detectable by the batter so that he will know what pitch is coming.