Why do we sometimes see the Moon in the Daytime?
There are two factors behind this phenomenon. First, the Moon is very bright. In fact, it is so bright that you can see it against the blue backdrop of the daytime sky. It is not as bright as sun, of court, because the Moon does not give off any light by itself. The Moon only shines by reflecting light from Sun. However, the Moon is one hundred thousand times brighter than the brightest nighttime star.
The Moon reflects so much light that our framing ancestors used its light to keep working to bring in the crops well into the night time hours. Hence, they named the full moon closest to the autumnal equinox the harvest moon. Once every four years, the harvest moon is actually in October. The full moon after the harvest moon is referred to as the hunter’s moon.
Theory of Full Moon
The second idea to consider is that the Moon goes around the Earth in a little less than thirty days, or what we call roughly a month. For part of that time, around the time of the full moon, the Moon is in the sky opposite the Sun. The Moon is rising as the Sun sets. But on each successive night the Moon comes up about an hour later. The Moon gets closer and closer to the direction of the Sun in the early-morning hours, finally appearing very close to the Sun in the sky around new moon time, rising and setting at about the same time as the Sun.
Then the Moon gets farther and farther from the Sun in the Sky each night until it gets back to full moon. The portion of the Moon that is lit up depends on the angle the Moon makes between the Earth and the Sun, which causes the various phases of the Moon.
During these phases, people on Earth can see the sunlight that strikes the Moon and is reflected from the Moon to us on Earth. So then we can see the Moon during the day. Again, if you see the Moon rising after sunrise, it is going from new moon to full moon, so each morning you see more and more Moon.
The Moon is out as many hours during the daytime as it is out during the nighttime. It is just that we associate the Moon with the nighttime sky. Of course, it is brighter in the night sky and hence more noticeable.
We use the Latin work Luna to refer to anything pertaining to Moon. Luna is a latin word etymologically related to Lucere which mean to shine. Now this moonshine is not the same as the illegal liquor by the same name.
Experiment to prove the Phenomenon
Get a softball, a basketball and lamp. The lamp is the Sun, face the lamp and hold the basketball (Earth) in front of it. As you move the softball (Moon) around the basketball, you will be able to see all the phases, and will also see that the Moon is visible during the daytime hours. Mentally and physically put yourself in place of the basketball. As the softball Moon goes around your head, you will be able to see the Moon in the daytime. Remember that daytime for you is when your eyes can see the Sun.