Normal is the other half of an action-reaction pair
If a person is sitting on a chair , there must be a gravitation force acting in downward direction which is equal to the weight of that person . That means the person is exerting a force on the chair equal to its weight . But the person is not falling down the chair , because of newtons third law of motion .
There must be a counter force which is equal and opposite to the force exerted by the person on the chair , in order to make net force equal to zero and to make that man in stationary state ( no movement ) .That force is called Normal force which is been acted by the chair on the person .This implies Normal is the other half of an action-reaction pair