It's All in the Legs!
No surprises - most running injuries affect the lower limb!
Very seldomly do injuries occur in isolation, often being down to a combination of a change in biomechanics, loading, and bad luck!
The key objective in running rehabilitation is not only returning you to your regular street slog, but also protecting you against future potential injury where possible.
Strength? Power? What do you mean..?
Strength is the body's ability to produce force. The stronger you are, the more force you produce, from whichever muscle you are measuring. Think strongman challenges and arm-wrestlers!
Power is the ability to change the force produced by your muscles over time - the shorter the time and the greater the change in force, the more power you are able to produce. Think javelin throwers, and sprinters, where acceleration is important.
There are many ways to waste energy during running. While running, your Centre of Gravity (CoG) is moving up and down, and side to side. The more you move your CoG up and down and side to side, the less efficient you are.
BUT: your body is not designed to manage the loads imposed during running without moving your CoG - your tissue will break down as the load will exceed your ability to adapt to it.
So it is a balance between soaking up some of the force to prevent overload, and transmitting that force into your body to permit forward motion.
Improving strength (in your muscles, bones, ligaments, cartilage etc) and power (in your muscles) gives you greater control of your CoG, and more ability to manage the running load.