A dipole moment is a quantity that describes two opposite charges separated by a distance. It is a quantity that we can measure for a molecule in the lab and thereby determine the size of the partial charges on the molecule (if we know the bond length). By definition the dipole moment, μ, is the product of the magnitude of the separated charge and the distance of the separation:
where \(q\) is the magnitude of the separated charge and \(r\) is the distance between them.
If we were to use SI units, charge would be in Coulombs and distances in meters. However, the charges were are talking about in molecules are very small (partial electron charges) and the distances are tiny as well (less than 1 nm). So this would lead to dipoles that are very, very small. So instead we use another historical unit, the Debye. 1 Debye is approximately 3.33 x 10-30 C*m. Molecules typically have dipole moments around 1 D.
If a molecule has a dipole moment, then we call it "polar." However, how big does the dipole have to be? Can it be 0.0001 D? That is ten thousand times less than a molecule with a dipole of 1 D. There is no strict cutoff. Nonetheless, molecules with atoms with very small electronegativities differences typically will have bonds that are only very slightly polar. This will lead to overall dipole moments for the molecule that are very, very small and would be considered non-polar. The most important example of this is hydrocarbons, molecules that contain hydrogen and carbon. While H and C don't have identical electronegativities, they are very close. So the C-H bond is very, very weakly polar. Overall, chemists (and biologists) would consider hydrocarbons to be non-polar (even though technically they might have very tiny dipole moments).
Most important when determining if a molecule has a dipole moment are two factors. One it must have polar covalent bonds. Two, it must have a shape in which all the dipoles don't cancel. Thus, our great interest in the shapes of different molecules.