"Aldarion and Erendis" stands out in the corpus of Middle-earth texts for various reasons. For one thing, it is the only story of any detail set in Númenor before the end of that island (the tale of its end is found in The Silmarillion as "The Akallabêth). It takes place in the earlier years of the Second Age, shortly after the Númenóreans began sailing back to Middle-earth for the first time and before Sauron forged the Rings, sparking war with the Elves. The preceding "tale" in the collection, "A Description of the Island of Númenor" functions as a companion piece to "Aldarion and Erendis," fleshing out the geographic and cultural environment of the Númenor of their tale.
"Aldarion and Erendis" is also unique among Tolkien's works because the chief source of its drama is the marriage of the titular characters: Tar-Aldarion the 6th King of Númenor and his wife, the only commoner-born Queen of that land. Mind you, while this marital drama is forefront, the tale is not solely about the tragedy of one family. "Aldarion and Erendis" shows how the earliest seeds of the Akallabêth were laid, what Tolkien called "the shadow of the shadow" that would later fall on Númenor. As the great ship-king of Númenor, Tar-Aldarion's reign laid the foundations for his people's intervention into the later war of Sauron and the Elves, paving the way for the destruction of Númenor at Sauron's conniving and the involvement of Aragorn and Gondor in The Lord of the Rings.
One particular point where "Aldarion and Erendis" converge with Aragorn's tale is the White Tree of Gondor. In The Lord of the Rings we learn that the White Tree, the symbol of Gondor's kings, is descended from a tree on the Elven island of Tol Eressëa. For so long as a descendent of that tree blossoms, the descendent of Elendil rule Gondor. In the same way that Elendil's people came from Númenor, the first White Tree of Gondor came from Númenor as a sapling. Its parent tree, cut down by Sauron in Númenor's last days, was planted during "Aldarion and Erendis"--a wedding gift from the Elves of Tol Eressëa. The prophecy connecting the tree to the kings would not come until later, beyond the scope of this story.
My vignette--and a simple vignette it is--for this story shows Aldarion and the tree. Aldarion's marriage fell apart when he went back to sea and returned several years late. Erendis had returned to her native part of the island and their house together in Armenelos, the royal city, was empty. Aldarion went to visit his wife once he returned, but they were both too proud to bridge the impasse between them and Aldarion returned to Armenelos in cold anger. He then ordered his house there destroyed. The text of this part of the tale, which comes near the point where Tolkien ceased to work on it, reads:
On the next day he gathered men in Rómenna and brought them to Armenelos. There he bade some fell all the trees, save one, in his garden, and take them to the shipyards; others he commanded to raze his house to the ground. The white Elven-tree alone he spared; and when the woodcutters were gone he looked at it, standing amid the desolation, and he saw for the first time that it was in itself beautiful. In its slow Elven growth it was yet but twelve feet high, straight, slender, youthful, now budded with its winter flowers upon upheld branches pointing to the sky.