The Horizon
The light of the sun emanates out from its surface in straight lines. Light can't go around corners, so when the Earth turns so that its horizon passes above the location of the sun, night comes quickly because there isn't any sunlight present when the mass of the Earth is between the sun and where you are standing. The sun is in the same place that it was before, but you are now on the opposite side of the Earth from the sun.
Sunlight
During the day, you can see because there is light coming down to the earth from the sun. Even on cloudy days when you can't actually see the sun, enough of its light gets through the clouds so that you can still see.
The Moon
Unlike the sun, the moon doesn't follow a straight path across the sky every day. This is because while the Earth is revolving around the sun, the moon is revolving around the earth. When the relationship of the Earth, sun and moon is right, sunlight reflects off of the moon and back onto the Earth, making the nighttime lighter than it would otherwise be.
Sunrise
Sunrise happens when the earth rotates far enough that your location on its surface is once again on the side where the sun is located. It still appears from the earth that the sun is traveling across the sky, but, as with sunset, this is an illusion caused by the rotation of the planet.