The shape of water
Water is the molecule worth working through carefully, because almost everything in the next section depends on it being polar.
Four pairs, of two kinds
The oxygen atom in a water molecule has four pairs of electrons in its valence shell. Two of them are bonding pairs, shared with the hydrogen atoms. The other two are lone pairs, belonging to the oxygen alone.
Those lone pairs push the two bonds closer together, so the molecule is not a straight line. It takes an angular shape, with the oxygen at the vertex.
Why it is polar
Oxygen is more electronegative than hydrogen, so in each O–H bond the bonding pair is drawn towards the oxygen. The oxygen atom therefore carries a small negative charge and each hydrogen atom a small positive charge.
The shape is what makes this matter. Because the molecule is bent rather than straight, the two positive hydrogens sit at one end and the negative oxygen at the other, so the molecule has a negative side and a positive side overall.
Water is a compound containing polar covalent bonds, and its angular shape leaves the whole molecule polar. That single fact is behind everything in the next section.