The rule of thirds in page design is a compositional guideline that divides the layout into nine equal parts using a grid overlay. By placing key elements along the intersections or along the lines, the design becomes more visually appealing and balanced. This technique can create a sense of movement and guide the viewer's eye through the page, making it more engaging and captivating. By following the rule of thirds, designers can achieve a harmonious layout that draws attention to important elements and enhances the overall aesthetic appeal of the design.