How does using the correct technique prevent injuries?

There are two main reasons to use correct form: First, the body is limited in its range of motion, and second, the body works better when the forces and movements are "aligned" in the way that allows the body to work best.

These two issues apply for all human physical activities, whether one considers sports or job activities, or simple day-to-day movement.

Here is some explanation of both reasons:

FIRST: human joints are not infinitely movable. Certain athletes (such as gymnasts and ballerinas) are very flexible, but even they cannot move their arms and legs in any way they please. Thus, proper technique ensures you do not exceed your own range of motion for your joints.

SECOND: Consider the body to be made up of a bunch of levers. Bones are the lever arm, and muscles provide the force to move the levers which in turn allow the body to do the physical things the body does. Levers essentially work in 2 dimensions -- up and down, and along the lever arm. When work is done along those dimensions, maximum force is provided through the least exertion, AND this happens to be the form of movement that results in the least strain on tendons, ligaments, and connective tissues inside joints. When work is done in a manner that includes the third dimension (consider "side to side" to be third dimension), all of the tissues in a particular joint are stressed, and may be over-stressed quite easily.

The result of this over-stress are often "soft tissue" injuries: tendonitis, sprains and strains, muscle tears. Occasionally the over-stress can result in broken bones, particularly the bones of the ankle and wrist.