In a closed moving train, moving with uniform velocity with respect to an observer on a station, the person in the train - here after we shall denote the person by the symbol A- will not know that he is moving.
A bob suspended by as string from the ceiling of the train will be vertical to the floor of the train.
Suppose the train now begins to accelerate. The bob will turn through an angle θ to the vertical. Since the train is a close one, A will infer from this this change in the vertical direction that his train is accelerating. He can calculate the acceleration from the angle and hence he will apply a force equal to mass times this acceleration to all the objects in his train.
This force is not the result of reaction force as far as A is concerned To apply Newton's laws of motion which is for inertial frames of reference, A applies this force to all objects in his train and thus makes his frame equivalent to an inertial frame.
This force which is not as a result of action reaction force [ with respect to A] is called pseudo force.
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