A benzene ring has six electrons delocalised over the ring. This can't be represented well by standard bonding models. It can be thought of as a 6 atom, 6 electron bond. It can also be considered as a resonance hybrid of the two Kekule forms. If we consider the 6 atom, 6 electron bond, this matches with the idea of an average of one of these electrons associated with each C atom at any time. However, this is also misleading in that implies that the carbon atoms have an incomplete octet and hence is highly reactive (both of which are wrong), or might be taken as having radicals (unpaired electrons) available for reaction, which is also untrue.
All of the measurements of benzene show that it has no single carbon-carbon bonds and also no carbon-carbon double bonds. The bond lengths are too long to be double bonds and too short to be single bonds. The reactivity is significantly different from both alkanes and alkenes. The 'ring current' associated with the electrons being delocalised over the ring is directly observable through 1H NMR.