A delocalized electron or electron pair is a freely moving electron pair that is responsible for different resonating structures. Since they take part in resonance it is important to note that the delocalized pair of electrons always occupy a standalone p orbital and not the hybridized orbital. Also, see Delocalization.
Consider the resonating structures for the Acetone anion. Notice that the carbon atom is sp2 hybridized and has the delocalized pair of electrons in a p orbital. This enables the formation of the pi bond in the structure on the right-hand side.