Frictional forces are intermolecular forces.  These forces act between the molecules of two different surfaces that are in close contact with each other.  On a microscopic scale, most surfaces are rough.  Even surfaces that look perfectly smooth to the naked eye show many projections and dents under a microscope.  The intermolecular forces are strongest where these projections and dents interlock resulting in close contact. The component of the intermolecular force normal to the surfaces provides the normal force which prevents objects from passing through each other and the component parallel to the surface is responsible for the frictional force.
Assume a cabinet is resting on the floor.  Nobody is pushing on it.  The intermolecular forces are normal to the surface.   The force of gravity  (red arrow) is balanced by the normal force (black arrow).
Now assume that you are pushing against the cabinet.  The cabinet is not moving, but the surface molecules are displaced by microscopic amounts.  This results in intermolecular forces which have a component tangential to the surface (the force of static friction).  This tangential component opposes the applied force.  The net force on the cabinet is zero.  The harder you push the greater is the microscopic displacement of the surface molecules and the greater is the tangential component of the intermolecular forces.
When you push hard enough, some of the projections on the surfaces will break off, i.e. some of the surface molecules will be completely displaced.  The horizontal component of the intermolecular forces diminishes and no longer completely opposes the applied force.  The cabinet accelerates.  But while the horizontal component has diminished, it has not vanished.  It is now called the force of kinetic friction.  For the cabinet to keep accelerating, you have to push with a force greater in magnitude than the force of kinetic friction.  To keep it going with constant velocity you have to push with a force equal in magnitude to the force of kinetic friction.  If you stop pushing, the force of kinetic friction will produce an acceleration in the opposite direction of the velocity, and the cabinet will slow down and stop.
The frictional force always acts between two surfaces, and opposes the relative motion of the two surfaces.
• The maximum force of static friction between two surfaces is roughly proportional to the magnitude of the normal force N pressing the two surfaces together.  The proportional constant is called the coefficient of static friction msThe magnitude of the force of static friction is always smaller than or equal to msN,   We write fs £ msN, where fs is the magnitude of the frictional force and N is the magnitude of the force pressing the surfaces together.  For the cabinet and the floor, N is the weight of the cabinet.  The coefficient of static friction is a number (no units).  The rougher the surface, the greater is the coefficient of static friction.  As long as the applied force has a magnitude smaller than msN, the force of static friction fs has the same magnitude as the applied force, but points in the opposite direction.

• The magnitude of the force of kinetic friction acting on an object is fk = mkN, where mk is the coefficient of kinetic friction.  For most surfaces, mk is less than ms.

Problem:

A racing car accelerates uniformly from 0 to 80mi/h in 8s.  The magnitude of the force that accelerates the car is approximately equal to the magnitude of the frictional force between the tires and the road.  If the tires do not spin, determine the minimum coefficient of static friction between the tires and the road.

• Solution:
• The magnitude of the acceleration is a = (80mile/h)/8s = (35.76m/s)/8s = 4.47m/s2.
The magnitude of the force accelerating the car is fs = ma = ms(min)N.  The normal force is N = mg.
We therefore have ma = ms(min)mg or a = ms(min)g, ms(min) = a/g = 4.47/9.8 = 0.46.