Since the atoms of most elements do not have full outer electron shells, they tend to react with one another to form compounds with a more noble gas like electron configuration. Not all chemical bonds fall fully under ionic or covalent, as there are many that lie somewhere between the two extremes. A polar bond is a covalent bond in which the individual atoms exert different attractions for the shared electrons. This results in an uneven distribution of charge and a molecule with one slightly positively charged end and one slightly negatively charged end.
The prime example of polar bonding is water. The Oxygen end has a slightly positive charge, while the Hydrogen ends are slightly negative. Other polar molecules dissolve readily in water, while non-polar molecules do not.