Explosive strength training has been recommended for competitive, elite runners for a long time. If you are a competitive runner, here's some research that might convince you to give it a try if you haven't already.
In a study at the Institute for Olympic Sports in Finland, researchers divided 18 elite, endurance athletes into two groups in which total training volume was the same for nine weeks. In one group, nearly a third of the training was replaced with explosive type strength training while the control group used only three percent of their training time for those techniques.
At the end of the nine-week period the experimental group who had trained with explosive strength exercises significantly improved their 5K times and 20-meter sprints as compared to controls, while their VO2max (a marker of aerobic potential) did not change.
The average runner, it must be remembered is not an elite, endurance runner such as those in the Finnish study. With that in mind, there is still much to be gained from an understanding of explosive strength training as long as you recognize that you must apply modifications and caveats carefully in order to avoid injury.
The caveat is that explosive strength training can be risky. The training techniques are very intense and your body should be well prepared with adequate strength and flexibility. You should have no sign of injury or pain, and you should begin any exercise with adequate warm up and stretching.
Any new training technique should be introduced carefully and gradually. Limit the time and the intensity of your first efforts. Build on those gradually if you remain symptom free. With a little care and wisdom, you can improve your speed.
A basic principle of training is specificity. In this case it means if you want to run faster, you have to run faster. This is not a redundancy, nor necessarily a statement of the obvious. Some runners may think that running more will improve your running time, but after your initial conditioning, that is not likely to be the case.
Sprint training is one form of explosive strength training that you can use right away to improve your speed-train faster to run faster.
Once a week substitute your usual run with sprint intervals. Go to the track and after warming up your muscles with a couple of laps treat yourself to a 50-yard dash. If you don't remember from your school days, a 50-yard dash is a full-out sprint, as fast as you can possibly go, but don't push yourself that hard in the beginning.
Work up to a full sprint over a period of several weeks or more. Take the same 50 yards leaping from one foot to the other with as long a stride as you can muster, shake it loose and try it again.
On another day out for explosive training, try 200-meter intervals-run 200 meters as fast as you can complete it, then jog a lap. Repeat. Workouts like these over time can increase your speed. If you're ready to set some new personal bests, give it a try, but always slowly and with care.