Answer
See the detailed answer below.
Work Step by Step
When you drive during the day there will be too much light reflected from the sun on the road. So when you turn on your headlights it would not be noticed by you, or the others, since the road is fully illuminated by the sunlight. So you can't see any additional light on the road.
This is similar to putting an extra cup of water into the ocean, the water increases is unnoticeable.
But during the night, the road will be illuminated by your headlights since they are already in the dark and you just illuminated them.
Now it is just similar to putting an extra cup of water into your car's radiator, you will notice the difference.
