When the object actually moves across the surface, the force is called kinetic friction force.
Friction is caused by the microscopic bonding and interlocking of the tiny bulges and indentations of one surface with another. One way of visualizing this is shown in the animation below.
As the purple rectangle moves rightward across the gray surface, the its microscopic dents bend the surface's microscopic dents rightward. In reaction, the surface's dents push leftward on the purple body's dents. This is the kinetic friction force that the surface applies to the moving body. More.