The moon's phases are caused by the relative positions of the sun, Earth, and the moon.
At any point in its orbit, the half of the moon facing the sun is always fully illuminated and the other half of the sphere is in shadow. From the sun, the moon always looks full, but from our vantage point on Earth, depending on where the moon is in its orbit, we can usually only see a part of the moon that's lit up, and sometimes none of it at all.
Once a lunar month, when the moon's orbit puts it between Earth and the sun, the part of the moon we can see is completely in shadow; we call this the new moon. Half a month later, when the moon is on the opposite side of Earth from the sun, the part of the moon we can see is fully illuminated; we call this the full moon.
Each night, from the new moon to full moon, more and more of the moon we can see is illuminated by the sun, and so from Earth we see the moon passing through its phases, gradually growing to a full moon and then shrinking again to a new moon.