Moving fast is about force production. The harder you can drive off the ground, the faster you will move. The stronger you are, the harder you can drive off the ground. Thus, the stronger you are, the more force you can produce, which directly translates into speed.
How do you get stronger? Specific adaptation to imposed demands. If you lift ever heavier, your body will adapt by becoming stronger. If you then apply that increased and ever increasing strength to ground force production (driving hard off of the ground), you will be faster. The faster you move, the more your body will increase its speed in order to keep up with the demands placed on it. As you move faster, your heart, lungs, and the rest of your cardio-pulmonary system are stressed and will increase its capacity by adapting to the demands placed on.
So, lift heavier=be stronger. Be stronger=move faster. Move faster=more endurance. Sounds like a winning combination for rugby, football, martial arts, wrestling, volleyball, handball, dance, surfing, firefighting, storming a house. Sounds like a winning combination for life.
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On the minute for 10 minutes:
10 Russian Kettlebell Swings 72/53#
50ft Overhead Plate Lunge (45/25#)/50m Sprint
30 Clean and Jerks 135/83#