Nature of friction while walking on the ground 
The frictional force between the feet of a man and the ground is static in nature.


These lines are taken from a reputed book. I was confused with this. Firstly, the feet is moving relative to the ground. So, why can't the friction be kinetic in nature. Secondly, for the frictional force to be static $f_s = ma$ , so while walking with constant velocity we get $f = 0$ but this cannot be true because we know that friction is necessary for walking.
Update
I deduced that:
The contact force exerted by the man on the ground and that exerted by the ground are action reaction pairs. When the vertical component of the contact force exerted on the man by the ground, exceeds the weight of the man, the contact is broken between man and ground and the contact force does not act. So, it can be concluded that the horizontal component of this reaction force acts for this time interval $dt$ when the foot is not moving relative to the ground. Hence the friction is static in nature.
But this raises some obvious questions : If friction acts only for this small time interval $dt$ at the point of contact(the feet of the man), can it affect the motion of the centre of mass of the man? Considering the part of the time the foot is in the air, does friction has anything to do with affecting the motion of the man? A force is always essential for motion. Since the only horizontal component acting on the man is friction, what exactly happens different while walking with constant velocity and while accelerating?
 A: 
Firstly, the feet is moving relative to the ground. So, why can't the
friction be kinetic in nature.

It would be kinetic friction if the feet were sliding or slipping on the ground. It is static friction that prevents the feet from sliding or slipping on the ground.

Secondly, for the frictional force to be static $f_s = ma$ , so while
walking with constant velocity we get $f = 0$ but this cannot be true
because we know that friction is necessary for walking.

Although the average velocity of the walker may be constant, it in reality consists of a series of accelerations and decelerations due to static friction between each foot and ground.
When you push forward on one foot static friction between that foot and the ground momentarily gives you an acceleration. When you land on the other foot static friction decelerates you. Then you push off on that other foot and the process is repeated. The average acceleration is zero and the average velocity of the walker is constant.
Hope this helps.
A: To clear your net force doubt:
Why does static friction come up? So your foot does not slide. You, through your muscles, have your foot push the ground. The static friction acts on your foot such that it cancels out the force your foot applies, so your foot remains at rest. However, your foot may be at rest, but the ground still exerts a force on you (by exerting it on your foot), which is what helps you move forward.

As for your edit:
As you push backwards on the ground with your foot, you will feel an acceleration forward. However, as you take your next step, you will decelerate, until you push your second foot against the ground hard enough to accelerate again, only to decelerate when you begin the next step. This deceleration happens because your foot is moving forward, so friction will actually push you backwards (to decelerate you). After that, you push your foot backwards, which is what accelerates you.
If you want to speed up your walk, then you simply push your leg into the ground backwards with more force, and get pushed by the ground backwards for less time by reducing the contact time.
A: See just like rolling motion of a ball, when you are walking, the part of foot which is in contact with the ground remains at rest. So while walking we do not move with respect to ground and friction remains static.
Now u know static friction is not constant. It changes according to the force acting on the body. When you walk push the ground backwards. The static friction pushes you forward in return, making you move forward.
