A starting point would be discussing populations that would benefit from using a speed ladder: beginners, youth and/or out of shape deconditioned individuals. You know what else would improve their general fitness, strength, power and endurance? ANYTHING! 

There are "speed" coaches out there who use the ladder drills with their youth population and see great results. Likewise trainers who use them with the elderly population and see an improvement in movement and balance. But I would argue they could perform a rudimentary movement pattern for an hour once a week and produce similar benefits. This holds true for individuals who has less than a year of formal training. 

The speed ladder is often used as a tool to improve athletic performance including speed and agility. Lets go over what speed and agility really means in the context of athletics. 

Speed involves covering more ground in a shorter period of time. If you can run 100 meters in less time after 1 month of training, you've improved your speed. The basic principles to improving speed is increasing stride frequency to go with stride length as a means of quantifying speed improvement. It's often thought of in more linear movements like the 40yard dash shown here by NFL Running Back Chris Johnson. 

Agility is your ability to change direction rapidly while being able to apply more horizontal force into the ground at an angle different than your current direction. To do this effectively your legs must be outside the vertical position of the center of your mass. If your center of mass doesn't move, you won't change directions. All you'll do is move your legs and not fall on your face. Agility often goes hand in hand with change of direction.

Anything we perform in the gym is done to improve general physical preparedness for athletics. Any result to tie-in athletic performance to a drill is pointless since there is a lack of specificity to the activity. Sports in itself is chaotic by nature, and running a linear pattern won't do much to get you ready for the reactive nature of the beast.. 

Speed and agility are based on rate of force, meaning if you go through the ladder at a sub maximal rate, you'll only improve your conditioning. Likewise any true speed training needs to be done with adequate rest periods, anything less than that you'll simply be performing cardio. For any training modality to work, it has to replicate or produce fundamentally similar benefits as the end goal. The S.A.I.D (specific adaptations to imposed demands) principle applies here, your training needs replicate force, rate of force application, metabolic and neural demands of an activity to have true carry over. 

Ladder drills can be very effective as a warm up for true speed training. It can help load and unload the muscles, tendons and incorporates some cardio. Technique needs to be the focal point, so skip the fancy footwork you saw on youtube.

Agility training involves a rapid change of direction from the initial direction of momentum. The most effective way to change direction involves having the legs move well outside of the vertical alignment of the center of mass, and driving into the ground at as horizontal of an angle as possible to create a strong drive against the ground. Momentum can also be overcoming inertia if you aren't already moving. This rapid change from no movement to movement could be considered a “first step,” which does not fall neatly under traditional speed training. The best example of agility would be NFL great Barry Sanders, always amazing to watch!

While ladder drills involve a rapid change of direction from one position to another, the direction one applies force is more linear than horizonatal. As a result any movement outside the center of mass is usually pretty tiny compared to more conventional agility training. Ladder drills would work well as a warm up for the same reasons mentioned above for speed, but in terms of developing higher levels of agility, it may not be as beneficial. It could be incorporated in sub-maximal workouts to involve some change of direction with low loads to stay sharp.

Like with the smith machine and bosu ball, every tool has a job in the gym. The ladder is great when used appropriately. It does very little to build top end speed, agility or quickness compared to conventional training. Relying on the speed ladder as a main cog to your training might actually make the athlete slower.

It's great when used for conditioning, rehabbing and as a warm up for much higher impact movements but as a stand alone training tool, it won't make you an Olympic sprinter any time soon.