Although there is a lot of research on the subject you wont find exactly how the biochemical mechanism works. The body is an incredibly complicated system and knowing every detail is not going to happen at the level of science knowledge available. Currently there isnt very much to the science of exercise, meaning that it is nowhere near completely fleshed out. It is very much still an art at this point.
It can however be explained in a simplified top-down approach based on things that we do know. Going any further is pretty much mental masturbation (knowing for the sake of knowing) and more than likely will not help you acheive your fitness goals.
Reducing your 40' or 100m dash is a matter of power to weight ratio barring technique. Increase your power and/or decrease your weight and you will be faster. Improving poor running technique can improve your times too, but mostly likely only slightly.
Reducing your 2k or 5k run would be a matter of improving your endurance/muscle activation byproduct removal systems and strength/weight ratio, barring technique.
Improving power is a matter of learning how to move heavier weights quickly. A well programmed strength and power oriented weight training routine that include copious amounts of olympic lifts would work here.
Improving strength is a matter of leanring to move heavy weights. A well programmed strength oriented weight training routine that includes copious amounts of squats and deadlifts would work here for running.
SAID Principle - specific adaptation to imposed demands - this principle is developed from observed evidence. You must do that specific thing to improve that specific thing. If you want to improve your running, you must run with ever increasing goals.
A good start would be Starting Strength by Mark Rippetoe and Lon Kilgore. It involves a linear progression compound functional exercise routine specifically designed to improve strength as quickly and efficiently as possible in those that are new and relatively new (some people have been lifting for years but are still considered beginners in terms of recovery) to strength training.
Practical Programming by Mark Rippetoe, Glenn Pendlay, and Lon Kilgore goes beyond Starting Strength and moves into the details of exercise programming and basically gives you the knowledge to provide a lifetime of productive efficient strength training.
Mark Rippetoes work is primarily stregnth oriented but includes aspects of power training because they have a significant overlap. However if you want to get into power specific training you need to find information specific to olympic lifting or throwing (shot put, hammer throw, javelin toss (or whatever), etc.). Mike Burgener is a good source for olympic lifting. You can find a lot of videos of different exercises including olympic lifting as well as excellent overall general fitness information at the crossfit.com website.