Why is the intensity value of an earthquake more meaningful than magnitude to a nonscientist?

The strength (more correctly termed magnitude) of an earthquake is a measurement of the energy released when the earthquake occurs.

The intensity however is derived based on the perceived level of ground shaking at a specific location and is a function of the amplitude of seismic waves at a given point and the damage they cause. The damage caused is in turn related to the local ground conditions and the specific construction techniques followed in the area.

Therefore for earthquakes of equal magnitudes, the location of the earthquake's epicentre in relation to centres of population is important. A high magnitude earthquake that occurs far from a populated area will do less damage than an lower magnitude earthquake in very close proximity to a populated area. As such the earthquake would have a lower magnitude but a higher intensity.

Secondly, ground motion and the amplitude of seismic waves is strongly dependent on the medium through which they travel. Seismic waves in hard rock masses (e.g. granite) have lower amplitudes than those that travel through soft ground such as sediments and so a building constructed and founded on hard rock is less likely to be damaged. As such a lower magnitude earthquake affecting structures founded on softer sediments may ultimately cause more damage than a higher magnitude earthquake affecting structures founded on hard rock. Again this would mean that in this specific case the earthquake of equal or lower magnitude would have a potentially greater effect on structures founded on soft soils and so the the intensity would be higher.

For more information, please see the related question.