Resonance is a way of describing the structure of a molecule when no single Lewis structure can account for all the observed properties of the molecule.
Resonance is a key component of valence bond theory and arises when no single conventional model using only single, double or triple bonds
Lewis dot diagrams often cannot represent the true electronic structure of a molecule.
While one can only show single, double, or triple covalent bonds using Lewis diagrams, one finds that the observed molecule does not match either of these structures but rather has properties in some sense intermediate to these.
You can think of resonance as approximation of the true electronic structure as a hybrid of single, double, or triple bond.
A great example of this is the structure of ozone: