By conjugated system we understand any arrangements of atoms that have a combined orbital spanning 3 (three) or more atoms. The simplest example of a conjugated system is the allylic system:
In such a system the pi bond is conjugated to an extra orbital containing 0 (cation), 1 (radical), or 2 (anion) electrons.
Another typical conjugates system that you need to know well is the 1,3-butadiene:
The following topics will go into more details of these types of compounds and their chemistry.