Dictionary Definition:

“The property of having a molecular structure which cannot equitably be represented by a single structural formula but is a composite of two or more structures of higher energy. ”

Selected from OxfordDictionaries.com

Functional Definition:

Resonance can be understood as a structural relationship where a molecule has a region that is the total sum of a double and a single bond. That molecule is considered more stable because the electrons between the atoms that make the bonds are more equally shared.

The figure shows the bracketed resonance structures of benzene each with alternating double and single bonds. The bottom benzene with a circle inside of its 6-carbon ring is the sum of both resonance structures. We write resonance structures as broken up, separated by arrows and bracketed to indicate that they are parts of a sum.

Figure courtesy of Dann Obermiller of StackExchange