Significance of the green stone?

[Lostgaeriel]

Oh, Ilúvatar!

Did Galadriel give Aragorn the Elendilmir? A long time before...

‘It came to pass that when Aragorn was nine and forty years of age he returned from perils on the dark confines of Mordor, where Sauron now dwelt again and was busy with evil. He was weary and he wished to go back to Rivendell and rest there for a while ere he journeyed into the far countries; and on his way he came to the borders of Lórien and was admitted to the hidden land by the Lady Galadriel.
‘He did not know it, but Arwen Undómiel was also there, dwelling again for a time with the kin of her mother. She was little changed, for the mortal years had passed her by; yet her face was more grave, and her laughter now seldom was heard. But Aragorn was grown to full stature of body and mind and Galadriel bade him cast aside his wayworn raiment, and she clothed him in silver and white, with a cloak of elven-grey and a bright gem on his brow. …

- Appendix A, (v), HERE FOLLOWS A PART OF THE TALE OF ARAGORN AND ARWEN

Or was that a different gem and/or only a loaner?

But back to the significance of the green stone...and the parallel to the graal made of emerald. (The 'holy grail' as a chalice in Arthurian tales is a fairly recent aberration.) Yes, green is a colour that can symbolize growth, rebirth and healing. And with the juxtaposition of the two names, Elessar and Envinyatar, the colour green is combined with its symbolic meaning and we see Aragorn as a vessel of healing powers - the graal.

His healing powers extend beyond curing physical and psychological injuries; Aragorn has the skills to heal, renew and recreate the kingdoms of Gondor and Arnor in a reign of peace and true security. Justice, pity, and mercy are the qualities shown by him in re-deploying the fearful soldiers on the way to the Black Gates, in making peace with the peoples of Harad, in setting free the slaves of Mordor, in his sentencing of Beregond, in giving the Forest of Drúadan to Ghân-buri-ghân and his people, etc.

And Aragorn hearing him, turned and said: 'Verily, for in the high tongue of old I am Elessar, the Elfstone, and Envinyatar, the Renewer': and he lifted from his breast the green stone that lay there.

- The Houses of Healing

How's that for pony dung?