The fragment shader answers one question, in parallel, millions of times per frame: what color is this pixel? Everything on screen funnels through one, and in shader-art practice the fragment shader often is the entire artwork, generating geometry-free imagery from coordinates, time, and math.
The form has signature techniques: distance fields for shapes, noise for organic texture, raymarching for 3D scenes without triangles, domain warping for the melted-liquid look. Audio-reactive work feeds analysis values in as uniforms, variables the shader reads each frame.
Post effects are fragment shaders too: bloom, grain, and color grading are per-pixel programs run over the finished image, which is how a whole look can change without touching the scene.