Because friction is when an object resists to another object moving on it.
The marble will stay there because an object at rest will stay at rest until acted upon by an unbalanced force and am object in motion will stay in motion until acted upon by an unbalanced force (such as friction)
The marble pushes back on the broom and the broom pushes back on the marble. When one object exerts force on a second object, the second object simultaneously exerts a force equal in magnitude and opposite in direction to that of the first object