What is lateral speed and agility?
It's the ability to accelerate, decelerate, stop and stabilize in any direction. As quick as possible. Without losing balance.
Think of Lionel Messi destroying world class defenders with feints and quick touches on the ball.
Steph Curry shaking an opponent out of his shoes with a quick crossover to a step-back three.
Barry Sanders juking and side-stepping his way through an entire linebacking corps.
Lateral speed requires plenty of coordination and body control, because you're constantly moving your center of gravity while changing direction at various speeds.
And it's also a key component to injury prevention, training players how to start and stop suddenly, without over-stressing the lower body joints.