This can be understood with Newton's law of motion. All objects, living and nonliving, have inertia - a tendency to remain in its present condition. That is, if a body is at rest, it will have a tendency to remain at rest in future. In the same way if the body is moving, it will have a tendency to continue its movement at a later time. This is described by Newton's law.
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If we stand at a point and jump, we will not be able to cover a good distance because our body will try to remain standing (be at rest), and we will have to spend a lot of energy to jump long distances.
To save on this energy, we run before jumping. As we run, we gradually change the state of our body from rest to a state of motion. As this happens over a period of few seconds, we need not have to spend a lot of energy. This reduces the power required to jump a long distance.