Most computers give you a range from 10-20 feet/3-6 meters. Fifteen feet is just a number in the middle of that range. If you understand why, it all makes sense.
More then 100 years of research indicates that if you ascend at a safe rate of speed, you should be able to go directly to the surface on an NDL dive. The safety stop is exactly what the name suggests--an extra precaution just to make sure.
You do not want your tissue pressure to be too great in relation to the ambient pressure around you, and that tissue pressure drops as you ascend. Ambient pressure drops dramatically in the last 10 feet, so in order to be sure you are in a safe range, it makes sense not to go shallower than 10 feet for this stop.
You have a variety of tissues in your body, and they absorb and release gas at different rates. The fastest tissues had the most pressure when you began the ascent, and by doing a safety stop, you will hopefully give them enough time to off-gas to a safe level. When they off-gas, they do so until they are at equilibrium with the pressure you are under at that depth--then they stop. In the meantime, some slower tissues are still on-gassing, even during the safety stop. That on-gassing will stop when they are at equilibrium with the pressure at that depth--they will not go beyond that.
In other words, if you stayed long enough at safety stop depth, all your tissues would end up at the pressure you are under at that depth--some will off-gas to get there, and some will on-gas to get there. The good news is that research on saturation divers indicates that if you are saturated at pressures shallower than 20 feet, you can go to the surface at any time. In other words, if you stayed at safety stop depth for a week, you could still go directly to the surface.