NAD(P)H experiences a conformational change when converted from the oxidised form to the reduced form. The nicotinamide ring distorts slightly, and this can be detected by enzymes, with the ring being in a different position. There is also the loss of a positive charge, and the addition of a hydrogen due to the reduction.
The movement on the reduction of NAD(P) allows the hydride to be in the desired location for the catalysis of the reaction it is involved in as a co-factor. This enables enzymes to exhibit specificity for the oxidised or reduced form.