Polar molecules have an imbalance of electron density due to differences in the electronegativity of their component atoms; nonpolar molecules generally have equal distribution of electron density.
To understand what makes molecules polar or not, we need to understand electronegativity and dipoles. The more electronegative (see the Pauling scale) an atom is, the more it’ll pull electron density toward itself and away from other atoms in the molecule. If there's no difference in electronegativity, the electrons will be shared equally and the bond between them will be nonpolar.
In this C—O bond, for example, the oxygen pulls electron density away from the carbon. This uneven sharing of electron density is called a molecular dipole, dipole moment, or dipole for short. Neither atom has a formal charge, but they each have a partial charge—this is distinct from an ionic charge, where an atom has full possession of an extra electron.
Water molecules are also polar because of the arrangement and electronegativity values of oxygen and the two hydrogen atoms.
Polar molecules have polar bonds in them, but there’s a catch! Let’s talk about a couple of examples.
These molecules are very similar, but they have very different polarity.
When determining if a molecule is polar, it’s important to consider symmetry. I’ve drawn all the partial charges and component vectors for each dipole here for visibility, but I combine them below.
The red dotted lines are planes of symmetry, and the blue arrows are dipole vectors (combined component dipole vectors). The left molecule only has one dipole, so it’s polar! The molecule on the left has two dipoles… so it’s extra polar, right? NOPE! The dipoles are completely equal and opposite in magnitude and direction, so this molecule is nonpolar.
Hopefully this quick guide helps clarify the difference between polar and nonpolar molecules. Remember that polar solvents will dissolve polar molecules and that nonpolar solvents will dissolve nonpolar molecules. For full coverage of this topic, including how molecular geometry affects polarity, check out my videos here!