NH3 is very polar, whereas NF3 is almost nonpolar. Why?

What we are really talking about here is electronegativity.  Electronegativity is a measure of an element's ability to attract neighboring electron density.  When looking at the periodic table, electronegativity increases across a row and going up in a column.  That means that electronegativity increases as you move to the upper right of the table and decreases as you move to the lower left.  Polarity within a molecule increases when neighboring atoms within the molecule have large differences in electronegativity.  NH3 (ammonia) contains a central nitrogen flanked by three hydrogens.  Nitrogen and hydrogen are far apart from each other on the periodic table which means that they have very different electronegativity values which in turn means ammonia is a polar molecule.  NF3, on the other hand, contains nitrogen and fluorine which are close to one another on the periodic table and therefore have similar electronegativity values which in turn means that NF3 is a very non-polar compound.