The moon is another one of Allah’s (swt) miracles. Not only the sun lights and illuminates our day, rather the moon lights our night too. The sun and the moon are created to serve mankind, they are two of Allah’s signs that none of His creations can claim them to himself or to any other.
The moon itself is not intended here, but its light that people see after the light of the sun disappears because the moon does exist even when the sun exists.
And the light of the moon is derived from the sun’s light; it is acquired from the sun’s rays when they reflect on it. Allah (swt) says:
{هُوَ الَّذِي جَعَلَ الشَّمْسَ ضِيَاءً وَالْقَمَرَ }
(It is He who made the sun a shining light and the moon a derived light) (Yunus: 5)