Polar molecules are molecules who's dipoles add together to give a net charge at each end of the molecule.
A good example of a polar molecule is water. Its bent shape arises from the two hydrogens being bonded on adjacent electron pairs, leaving 2 lone pairs adjacent to each other in orbit around the nucleas of the oxygen atom. This has the effect of bending the molecule into the shape you are familiar with.
Oxygen is a highly electronegative element meaning it has a strong attraction to electrons not in orbit around the nucleus (this is due to a combination of factors including a sizable number of protons in the nucleus and yet minimal electron sheilding, etc). The oxygen has the effect of attracting the shared pairs of electrons with the hydrogen atoms closer to it than they are to the hydrogen atoms, so there is more 'negativity' in the vicinity of the oxygen atom and more positivity in the vicinities of the hydrogen atoms. This is how dipoles are created.
As a result of the creation of these dipoles, the oxygen 'side' of the molecule (the top side I guess it would be in a conventional structural diagram although it doesn't matter when you draw it) would be more negative than the side with the hydrogen atoms on it. Hence, the molecule will be polar (it will have a slightly negative and a slightly positive end). Polar molecules can create dipole-dipole forces with other polar molecules (and dispersion forces with any molecules), and in some cases can form hydrogen bonds as well (a really strong type of intermolecular force resulting from strong dipole attractions involving hydrogen and flourine, nitrogen or oxygen).
Non polar molecules are where the dipoles created within the molecule 'cancel each other out' so there is no net charge at either end of the molecule. An example I think would be carbon dioxide, which is a linear molecule. The oxygens on each end 'pull' equally meaning the molecule as a whole remains neutral (and can only form dispersion forces with other molecules of it's type).
I hope that makes
some sense. Maybe one of the 02'ers could say something a little more relevant and concise?
Edit: I started this post, got distracted by some english and didn't finish it for ages so I didn't see Kini Mini's post before I made mine. Oh well I'll leave this here anyway.