An element's "desire" for electrons.  The more electronegative, the more likely it is to aquire electrons from other atoms to complete its shell.

F is the most electronegative element.  The closer to F on the periodic table, the more electronegative the element.  Electronegativity is effected by size, shielding, etc. 

Polar Covalent:  A polar molecule is situated so that it has either a partial positive or partial negative side.  Water is an example of a polar molecule as the hydrogen end is partially positive and the oxygen end is partially positive.

Ionic:  Bonding between [usually] a metal and a non-metal.  Non-metals are much more electronegative and therefor rip electrons off of their counterparts, giving both atoms a full charge and bringing them together.

Nonpolar Covalent:  Interaction between two non-metals [usually].  Elements "share" electrons in compounds so both shells may be completed.  However, if they are nonpolar, they are situated in such a way that here is no partial negative or partial positive area in the compound. 

Polar and Nonpolar compounds do not like to interact with one another.