Electronegativity is the strength of an atom to attract electrons to itself. The more electronegative an atom is, the greater the strength to attract an electron from another element and thus create a chemical bond.
When the difference in electronegativities is great, an ionic bond is generated. That is to say that one of the atoms has very little strength even to hold its own electrons while the other has a lot of strength and ends up stealing its electrons.
When the difference in electronegativities is not so great then neither of the two atoms has enough strength to steal electrons from the other atom, and they end up sharing their electrons with each other. This is called covalent bonding.
Now, polar and non-polar molecules are formed by covalent bonds. When electrons are being shared, the number of electrons that are shared may not be equal, this will make the charge of the molecule not equal on all sides, but it will be a little more negative on one side and more positive on the other, so it will be a polar molecule.
When the electrons are shared equally, the charge is homogeneous throughout the molecule, there is no side more positive than another, or more negative than another, then we say that the molecule is non-polar, this happens a lot with molecules formed with the same element, such as O2, N2, Cl2.