A polar bond exists between two atoms in which one atom has a larger electronegativity. As a result, electrons will spend more time around that atom and will make that end of the atom partially negative. The molecule is said to have a 'dipole moment' and this will make the molecule, as a whole, polar. An example of this is HF.
Non-polar molecules have no polar bonds OR have polar bonds that sum to give a dipole moment of zero.
In this first case, a good example is O2 - it is made up of homogenous atoms of the same type (oxygen atoms) with the same electronegativity. As a result, electrons do not spend more time around either end of the molecule and thus the molecule is non-polar.
In the second case, a good example is CO2 - a linear molecule. Although each C=O bond is polar, because of the shape of the molecule (being linear), the direction of polar bonds oppose each other and adding them yields a dipole moment of zero (it's like adding -1 to +1). Thus, the dipole moment not only depends on electronegativity, but on the shape of the molecule too.
H2S, like H2O is a polar molecule. Sulphur is more electronegative than Hydrogen and so in the H-S bond, the electrons spend more time around the sulphur atom giving it a partial negative charge. The shape of the molecule in this case is not linear, it is bent (for reasons beyond HSC level chemistry - if you really want to know look at VSEPR theory). Thus addition of the bond polarities doesn't cancel to give a dipole moment of zero and the molecule is polar.
Hope it helps!
