The Material modifier alters the base property with a new one taken from a given range mapped on the current material under the stroke.
You can use various properties of the materials, among which many are mono-component (i.e. give black-and-white results). In this case for the color modifier, an optional color ramp can be used to map these gray-scale values to colored ones. In the reverse case properties of the materials, which are multi-components (i.e. give RGB results) the mean value will be used for Alpha and Thickness modifiers.
If used with the Split by Material option in the Stroke tab, the result will not be blurred between materials along the strokes.