Sometimes,the moon appears as a round ball and sometimes,it looks like a sliver wedge.Sometimes,it appears as a half circle and at other times cannot be seen at all.This is because the moon changes its position in relation to the Earth and the Sun.This movement also changes the amount of light reflected back to the Earth from the face of the moon.Thus,we can see different phases of the moon.
The illustration may look a little complex at first, but it's easy to explain.
Sunlight is shown coming in from the right. The earth, of course, is at the center of the diagram. The moon is shown at 8 key stages during its revolution around the earth. The moon phase name is shown alongside the image. The dotted line from the earth to the moon represents your line of sight when looking at the moon. The large moon image shows what you would see at that point in the cycle. For the waning gibbous, third quarter, and waning crescent phases you have to mentally turn yourself upside down when imagining the line of sight. When you do this, you'll "see" that the illuminated portion is on your left, just as you see in the large image.
One important thing to notice is that exactly one half of the moon is always illuminated by the sun. Of course that is perfectly logical, but you need to visualize it in order to understand the phases. At certain times we see both the sunlit portion and the shadowed portion -- and that creates the various moon phase shapes we are all familiar with. Also note that the shadowed part of the moon is invisible to the naked eye; in the diagram above, it is only shown for clarification purposes. Finally, please realize this diagram is only meant to demonstrate how the phases work; the small inner moons in the diagram do not show the fact that the same side of the moon always faces Earth.
So the basic explanation is that the lunar phases are created by changing angles (relative positions) of the earth, the moon and the sun, as the moon orbits the earth.
If you'd like to examine the phases of the moon more closely, via computer software, you may be interested in this moon phases calendar software.
Moon Phases Simplified
It's probably easiest to understand the moon cycle in this order: new moon and full moon, first quarter and third quarter, and the phases in between.
As shown in the above diagram, the new moon occurs when the moon is positioned between the earth and sun. The three objects are in approximate alignment (why "approximate" is explained below). The entire illuminated portion of the moon is on the back side of the moon, the half that we cannot see.
At a full moon, the earth, moon, and sun are in approximate alignment, just as the new moon, but the moon is on the opposite side of the earth, so the entire sunlit part of the moon is facing us. The shadowed portion is entirely hidden from view.
The first quarter and third quarter moons (both often called a "half moon"), happen when the moon is at a 90 degree angle with respect to the earth and sun. So we are seeing exactly half of the moon illuminated and half in shadow.
Once you understand those four key moon phases, the phases between should be fairly easy to visualize, as the illuminated portion gradually transitions between them.
An easy way to remember and understand those "between" lunar phase names is by breaking out and defining 4 words: crescent, gibbous, waxing, and waning. The word crescent refers to the phases where the moon is less than half illuminated. The word gibbous refers to phases where the moon is more than half illuminated. Waxing essentially means "growing" or expanding in illumination, and waning means "shrinking" or decreasing in illumination