If you follow the octet rule, you know that an element must have 8 outside (or valence) electrons to be energetically favorable.
In CCl4, the carbon molecule forms four bonds; one for each chlorine atom. Each bond contains 2 electrons, so it is satisfied.
In PCl3, Phosphorous forms only 3 bonds with chlorine, which means in order to have 8 valence electrons, it also has a lone pair of electrons, not bonded with chlorine.
Now, in CCl4, picture the shape of the molecule like a plus sign, with the carbon in the middle and the chlorine at the four ends. It is symmetrical, and therefore is nonpolar.
In PCl3, the lone pair electrons push, so to speak, the 3 chlorine atoms away, making a T-shaped molecule. Since the chlorine is more electronegative than carbon, the molecule is unbalenced, making it polar.
