Geometry shaders allow processing and generation of additional geometry in the graphics pipeline, and can be used for optimizations like mesh refinement, level of detail adjustments based on distance from the camera, and culling of triangles outside the view frustum to improve performance. The document describes a sample application that combines these optimizations using geometry shaders, first refining geometry, then dynamically adjusting level of detail, and culling outside the frustum for an over 11x improvement in framerate. Geometry shaders require specific extensions and hardware support from modern graphics cards.