![enter image description here][1]


  [1]: https://i.sstatic.net/rUaWm.png
You see, if you're standing at the south part of the earth in this picture you can only see half the moon, also called a crescent moon, because the part that you can not see is facing the oppsite direction of the sun, therefore not receiving any sunlight.

You don't always see exactly half, sometimes you only see a thin strip of the moon, google for "crescent moon" and you'll see what I mean.