Why runners lean forward? Why runners tend to lean forward prior to start running? How does it help run faster? What is the physics behind his leaning? 
 A: Leaning allows for higher acceleration. If a runner at rest tries to run standing perfectly normal to the ground, he will never be able to move without falling over.  Leaning is necessary for accelerating, for a person whose centre of mass is higher up from the ground. 

Walking requires applying a force parallel to the ground to oppose friction, which generates a torque that tends to tip you over. Leaning provides a counter torque.

In a running race, there is a delicate interplay between these two torques. A runner has to balance both the torques to prevent falling.
Hence there is always a stable leaning angle, above which you fall forward and below which you fall backwards.

In a race, reaching your top speed quicker would increase your chances of winning. So it is beneficial to apply a significant force on the ground. But as you go faster, it becomes more and more difficult to exert a force on the ground. Because, doing so would require your legs to strike the ground more swiftly, which is limited by your physical capabilities.
Given below is a plot of the acceleration, velocity and distance versus time graphs of Usain bolt during his 100m race in 2008(taken from this site,). Though the scales of the axes may be different, this graph is typical for any human being.

Note that the acceleration, and hence force exerted by you on the ground, is highest at the beginning of the race, and it flattens out to zero after a while. 
At the beginning of the race, the torque due to friction is maximum. So runners would have to lean higher during this time, to counter it.

Also, the torque due to friction decreases as the race progresses. So it becomes necessary for you to decrease your leaning angle (and hence the counter-torque) when you near your top speed. The same principle leads to the 'straightening out' of runners in a race. (Video 1,Video 2)

In short, leaning at the beginning of the race enables you to reach your top speed faster, increasing your chances of winning. 
A: The weight applies to the center of mass (CM) of the person. When the person stands perpendicular to the ground, the force goes downwards. The normal force compensates the weight, so nothing happens.
However, when the runner leans downwards, the vector from the ground to his CM is not parallel to the weight force. That causes a moment of forces (torque) on the runner, which leads him/her to rotate around his/her feet (towards the ground). In short: if (s)he leans forward, (s)he can fall forward and hit the ground.
This would happen if we had only one point touching the ground, but we've gout our entire feet to avoid rotating and falling.
The thing is taht the torque creates a small angualr acceleration because the gravity force creates an acceleration. One component of this acceleration will be compensated by the normal force. The other component will be forward, and that makes us easier to start running. The gravity force does the effort for us.
