While the original Temple Menorah was lit in the day, the mitzvah of lighting the Chanukah Menorah, as explained in the Talmud, is to do so specifically at nightfall.
Why?
Because the message of the Chanukah Menorah is to light up the darkness of the world, to the point that even the places (or aspects of life) which were once dark, begin to radiate with a light of goodness and holiness! This applies to both our personal lives and personal challenges as well as to the world at large. Instead of battling the darkness, we introduce a good and holy light and help make the world a better place.