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.
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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.