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One interpretation would be the literal appearance of sunshine in the forest.
"... as with a sudden smile of heaven, forth burst the sunshine, pouring a very flood into the obscure forest, gladdening each green leaf...Such was the sympathy of Nature...with the bliss of these two spirits!"
Another, less obvious interpretation would be the sunshine and joy that permeated Hester and Dimmesdale, as they embraced their future..... and let go of the past.
"...a glow of strange enjoyment threw its flickering brightness over the trouble of his breast...His spirit rose...and attained a nearer prospect of the sky... " (Dimmesdale)
"... her youth, and the whole richness of her beauty, came back from what men call the irrevocable past...and [she experienced] a happiness before unknown..." (Hester)
The Scarlet Letter