OK, the easiest way to explain this one is with a demo. Sit facing a lamp. The lamp with be the Sun, and you will be the Earth. Hold a round ball, orange, etc. in one hand. It will be the Moon. We are simulating daytime, so face towards the lamp. Hold the ball out in front of you, and notice that you are looking at the dark side, which means that it is a new moon.

Now, turn to the left or right, so the Sun is low in the "sky." Hold the Moon out in front of you, and you will notice that although it is still "daytime", part of the moon is illuminated by the "Sun". By turning, you should be able to find several positions where you can still see the "Sun", but can also see a large part "Moon" that is lit up.

As you experiment, you will find that the farther the "Moon" is from the "Sun", the more of its face will be illuminated. At the extreme, you will notice that full moons rise as the Sun sets.