Overprinting refers to the screen-printing technique of printing ink directly on top of another ink, either done as wet-on-wet or wet-on-dry. Overprinting is done to create additional colors or different shades in the design other than the colors of ink that were used for the print. The artists determine what colors will be overprinted by cutting the overlays to reflect that.
If overprinting is done with transparent inks, a color other than what was originally printed will result because transparent inks allow light to pass through them. For example, if a transparent blue ink is printed over yellow ink the resulting visual color is green. If transparent red is printed over blue the resulting visual color is purple.
If overprinting with opaque inks, color variances are achieved in a different manner. Since opaque inks don't allow light to pass through them, an opaque ink printed over another ink will not produce another color. The ink that is on top is the color that is seen. To create other colors with opaque inks the artists must rely on optical illusion (e.g., printing a solid layer of yellow, then printing a pattern with blue ink over it results in the illusion of green).
Source: "The Encyclopedia of Garment Decorating"