When a solid substance is dissolved in water and causes a bulb in a conductivity apparatus to light up, it indicates that the solution is likely ionic. Ionic compounds dissociate into ions when they dissolve in water, allowing the solution to conduct electricity. The presence of free-moving ions in the solution is what leads to the bulb lighting up.
If you were to add water to the solution after conducting the initial test, you might expect the conductivity to either remain the same or even decrease slightly, depending on the concentration of the ions. Diluting the solution with water increases the volume but decreases the concentration of the ions. If the bulb lights up brightly when the solution is concentrated, adding more water may lead to a dimmer light because the ions are further apart and there are fewer charged particles available to conduct electricity.