Adding the lights is the first step toward a Whitted raytracer. For each ray that hits an object, several rays can be cast, reflection, refraction and shadow. The last one is the one created with lights.
Lights and shadow rays
Without light, objects are bland, seem to have no depth, … Light on a scene can be cast by several light sources. When a ray of the camera hits an object, the intersection point can be illuminated by one or several of those sources. Each of them contributes to the color of the object. If the light source direction is parallel with the normal of the object at the intersection point, the contribution will be maximum. If it is orthogonal, the contribution will be zero. The scalar product is the tool used to compute this quantity.