Why friction force peak just before the object moving? 
This diagram shows the amplitude of friction force of a typical contact-surface object. The friction force increases as we apply an internal force until it reach a maximum value just right before the object starts to move, and then it drop SHARPLY and remains constant as long as the object is still moving.
Could you explain all of physical interactions involve in that crucial moment just before the object begins to move which result in a diagram above?
 A: The idea here is that static friction is larger than dynamic friction. This is something that depends on the nature of the materials in contact and is not in general true because friction is not a fundamental force: it is a result of some very complicated phenomena at a microscopic level.
An explanation that does make sense to me is to think of the two objects in contact as having little peaks and valleys that fit into each other. To start the motion, you need to give a large enough force to get the largest peak out of the largest valley. However, once things are moving, the object has "broken free" and you can see that the motion of the body also contributes to getting in and out of the valleys i.e. you need to apply a smaller force.
This is one model but there are others out there that give you the same result. The way I would prefer to think of it is that it is an experimental fact that there is some sort of "sticking together" that you break when the object is set into motion and this is the difference between static and dynamic friction. 
