Under the framework of valence bond theory, resonance is an extension of the idea that the bonding in a chemical species can be described by a Lewis structure.  For many chemical species, a single Lewis structure, consisting of atoms obeying the octet rule, possibly bearing formal charges, and connected by bonds of positive integer order, is sufficient for describing the chemical bonding and rationalizing experimentally determined molecular properties like bond lengths, angles, and dipole moment. However, in some cases, more than one Lewis structure could be drawn, and experimental properties are inconsistent with any one structure.  In order to address this type of situation, several contributing structures are considered together as an average, and the molecule is said to be represented by a resonance hybrid in which several Lewis structures are used collectively to describe its true structure.  For instance, in NO, nitrite anion, the two N–O bond lengths are equal, even though no single Lewis structure has two N–O bonds with the same formal bond order. However, its measured structure is consistent with a description as a resonance hybrid of the two major contributing structures shown above: it has two equal N–O bonds of 125 pm, intermediate in length between a typical N–O single bond (145 pm in hydroxylamine, HN–OH) and N–O double bond (115 pm in nitronium ion, [O=N=O]).  According to the contributing structures, each N–O bond is an average of a formal single and formal double bond, leading to a true bond order of 1.5.  By virtue of this averaging, the Lewis description of the bonding in NO is reconciled with the experimental fact that the anion has equivalent N–O bonds.
The resonance hybrid represents the actual molecule as the "average" of the contributing structures, with bond lengths and partial charges taking on intermediate values compared to those expected for the individual Lewis structures of the contributors, were they to exist as "real" chemical entities. The contributing structures differ only in the formal apportionment of electrons to the atoms, and not in the actual physically and chemically significant electron or spin density.  While contributing structures may differ in formal bond orders and in formal charge assignments, all contributing structures must have the same number of valence electrons and the same spin multiplicity.
Because electron delocalization lowers the potential energy of a system, any species represented by a resonance hybrid is more stable than any of the (hypothetical) contributing structures. Electron delocalization stabilizes a molecule because the electrons are more evenly spread out over the molecule, decreasing electron-electron repulsion. The difference in potential energy between the actual species and the (computed) energy of the contributing structure with the lowest potential energy is called the resonance energy or delocalization energy.  The magnitude of the resonance energy depends on assumptions made about the hypothetical "non-stabilized" species and the computational methods used and does not represent a measurable physical quantity, although comparisons of resonance energies computed under similar assumptions and conditions may be chemically meaningful.
Molecules with an extended π system such as linear polyenes and polyaromatic compounds are well described by resonance hybrids as well as by delocalised orbitals in molecular orbital theory.