Yes, there are day and night on the moon, but not the same as our planet. Instead of twenty-four hours, a moon-day is equal to 27.3 earth-days because the moon takes so much time to complete a rotation around its axis. What is more surprising is that the moon takes exactly the same amount of time to complete a circle around the earth too, i.e. 27.3 days. As a result we always see only one side of the moon. At the most 59% of the moon’s surface is visible from the earth. The rest 41% of the surface is never seen by us.
Furthermore, the moon only has a day and a night, and no evening! The reason: There is no atmosphere on the moon. Due to the absence of air the sun-rays do not scatter at all. Hence, where the sun-rays fall there is a dazzling light and the rest is extremely dark! As if sunshine and darkness are partitioned by drawing a line between them. In the same way without air the climate is also not temperate on the moon. The temperature in the light would be 102°C, whereas an inch away in the dark the mercury would drop down to freezing -157°C!
Lunar day (Wikipedia)