The meaning of Walden being a perfect forest mirror is related to the purity and peace the author describes. The sky and the Earth joined as one, with no fences between them, like a mirror.
The sky is a reflex of Earth, and the meaning of this excert is showed in the sequence ";<em> -- a mirror in which all impurity presented to it sinks, swept and dusted by the sun's hazy brush -- this the light dust-cloth -- which retains no breath that is breathed on it, but sends its own to float as clouds high above its surface, and be reflected in its bosom still." (Thoureau, chapter 9).</em>
<em> </em>Thoureau went to live in the forest in order to discover himself the essentials of life.
Lincoln's message in his Gettysburg Address was that the living can honor the wartime dead not with a speech, but rather by continuing to fight for the ideas they gave their lives for.