How does incident light that falls on an object affect the motion of electrons in the atoms of the object?

Incident light makes an electron oscillate. The electrons emit light or absorb the light, collide with other electrons, thereby converting light energy to more internal energy. and convert it to heat.

Light wave of a given frequency is incident on a material with electrons having the same vibrational frequencies, then electrons absorb the energy of the light wave and transform it into vibrational motion.