Simbelmynë is a white flower. It means 'evermind,' literally, and is often found along gravesites because those buried there are 'ever (in the) mind(s)' of their loved ones.
Gandalf points them out in Edoras as they observe the tombs of Rohan's fallen kings:
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'Look!' said Gandalf. 'How fair are the bright eyes in the grass! Evermind they are called, simbelmynë in this land of Men, for they blossom in all the seasons of the year, and grow where dead men rest. Behold! we are come to the great barrows where the sires of Théoden sleep.'
'Seven mounds upon the left, and nine upon the right,' said Aragorn. 'Many long lives of men it is since the golden hall was built.'
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This is why Aragorn says what he does later - note the part of the quote you left out, speaking of the 9 and 7 mounds:
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Aragorn did not touch him, but after gazing silently for a while he rose and sighed. ‘Hither shall the flowers of simbelmynë come never unto world’s end,’ he murmured. ‘Nine mounds and seven there are now green with grass, and through all the long years he has lain at the door that he could not unlock. Whither does it lead? Why would he pass? None shall ever know!
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What Aragorn is saying is that the flowers will never grow there, meaning no one shall ever know his intent, mourn his loss, or keep him in memory (he being the body they find at the door); some are remembered (as the kings are) and some pass with no one's notice (the body Aragorn finds).
They're also mentioned in the appendices:
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'Helm was brought from the Hornburg and laid in the ninth mound. Ever after the white simbelmynë grew there most thickly, so that the mound seemed to be snow-clad. When Fréaláf died a new line of mounds was begun.'
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