What I believe they actually mean is they want to be faster and move better.
I mean Michael Flatley, Lord of the Dance has extremely fast feet but he doesn’t actually move anywhere. His ‘foot speed’ is useless as a lacrosse player (his outfit on the other hand…). All he is doing is picking his feet up really, really, really quickly.
To move, you must apply force into the ground. The more force you can apply, the faster you will move.
Al Vermeil is the Strength Coach for the Chicago Bulls and easily one of the best of all time (backed up by his handful of Championship Rings he has from teams he trained). He has a very simple take on Speed: Get Stronger! The stronger you are the more force you can apply into the ground.
Ladder Drills are good for improving coordination and can be used as part of a dynamic warm up to get the Central Nervous System fired up.
Agility Drills are good for teaching technique of movement and proper planting and multi-directional movements.
Acceleration Drills are good for improving running technique and teaching you to be in better position to apply force.
However all those drills will only do some much to help your ‘foot speed’ if you aren’t getting stronger!
You need to be able to apply more force to go along with your improved technique.
So get stronger!