We can physically move vertices in the vertex shader to create wave effects. If your meshes are too low-poly, you can subdivide them with tessellation to improve the fidelity.
Along with coloring pixels, we can modify the vertices of a mesh in-shader to create wave displacement effects, amongst other things.
Problems can often be solved in several ways. We can draw grass with basic meshes, geometry shaders, procedural rendering, billboards, terrains, and impostors.
Geometry and tessellation shaders are capable of drawing thousands of grass blades on top of a ground mesh. Based on a fantastic article by Roystan.
