A geoboard is a mathematical manipulative used to explore basic geometry concepts like perimeter, area, and characteristics of shapes. It consists of a board with nails half-driven in at intervals in a grid pattern. Rubber bands are wrapped around the nails to form shapes. The document provides instructions to make a geoboard using a thermocol sheet with pins inserted at 1-inch intervals in a grid, and then uses it to form a rectangle and calculate its area to verify the area formula for rectangles.