The most common example of this is in benzene rings, C 6 H 6 . The six carbons are in a hexagonal arrangement, all in the same plane. There are two possible ways to draw this structure so that all of the valences are filled, using a combination of single and double bonds. These are shown below. Hydrogens are left off for convenience, and each of the corners is a carbon atom.
Single lines are single bonds, double lines are double bonds.
Count the bonds and satisfy yourself that, with the addition of six hydrogens, all of the carbons have full valences. However, now we have a different problem. This is where aromaticity comes in. Since the resonance structures are equally probable, benzene rings do not exist in exactly either state, but in a mixture of both. This makes all six bonds a little more than single bonds and a little less than single bonds.