Looking down on the earth moon system 
from the North Celestial pole. The sun is to 
the right 

The phases that we see from earth when the 
moon is in the same positions as in the 
diagram above. Again, the sun is to the right

Lunar rotation
The moon always turns the same face towards the earth. This is only possible if the moon rotates once for every time it orbits the earth, one rotation for every one revolution. This is called synchronous rotation
Lunar revolution 
Because the moon revolves around the earth, and its position relative the earth and the sun changes  every moment, we see different amounts of the same face of the moon being lit from the earth, i.e., we see the moon going through its phases. 

It is important to realize that just like the Earth, half the moon is lit at all times, and there is no dark side to the moon. (What we call the dark side is really the side that is always facing away from us and that we never see from the earth) 
Phases of the moon 
What we see from the earth as the moon revolves, is a varied amount of the face that is always towards us being lit. When the moon is between the earth and the sun, the lit side is facing away from us and we cannot see the moon, it is a new moon. Progressively, as the moon revolves, we see more and more of the face being lit, the moon is growing, waxing. It waxes from a sliver, a crescent, through half the surface being lit, a first quarter, to more than half the surface being lit, a gibbous moon, till it is full. From the full moon, the lit part decreases again, it wanes through a gibbous phase to third (or last) quarter and a waning crescent to again disappear as a new moon.