I am trying to learn Blender. While trying to render a subdivided plane with an image texture applied to it, the subdivision edges are not removed in the rendered result.
Kindly, advise, why these edges appear in the render.
It should be obvious that a texture with lines in it is going to render with those lines.
The Export UV Layout operator exports the UVs as lines so you can use it as a guide for texturing in external programs. (In your question you should not even need it, because you are just texturing a plane.)
In any event you must turn off the UV guide layer in your project (in whatever image editor you are using) before exporting the texture map to use back in blender.