In theoretical chemistry, a conjugated system is a system of connected p-orbitals with delocalized electrons in a molecule, which in general lowers the overall energy of the molecule and increases stability. It is conventionally represented as having alternating single and multiple bonds. Lone pairs, radicals or carbenium ions may be part of the system, which may be cyclic, acyclic, linear or mixed.  The term "conjugated" was coined in 1899 by the German chemist Johannes Thiele.
Conjugation is the overlap of one p-orbital with another across an adjacent σ bond (in transition metals, d-orbitals can be involved).
A conjugated system has a region of overlapping p-orbitals, bridging the interjacent locations that simple diagrams illustrate as not having a π bond. They allow a delocalization of π electrons across all the adjacent aligned p-orbitals.
The π electrons do not belong to a single bond or atom, but rather to a group of atoms.
Molecules containing conjugated systems of orbitals and electrons are called conjugated molecules, which have overlapping p orbitals on three or more atoms. Some simple organic conjugated molecules are 1,3-butadiene, benzene, and allylic carbocations. The largest conjugated systems are found in graphene, graphite, conductive polymers and carbon nanotubes.