Yeah, Google translation is not to be completely trusted(generally, not just for Greek language or this song), but it helps with the connection between us all.
“Tzivaeri” actually comes from Turkish language, Arab before that. It means -indeed- a precious stone, a treasure, so "my tzivaeri" means "my treasure". But, the song is Greek.
It is one of the most beautiful songs from Dodecanese( A group of Greek islands between Asia Minor and Crete. This group also contains small islets, one of which is “Imia” that you read about in one of my stories and asked.)
Ξενιτιά means the foreign lands, but even like this, the phrase doesn’t give the depth of the meaning, which is the "forced to be away of your roots" somehow( forced by others, or by the circumstances).
So, it is an emigration song which expresses a mother’s sorrow for her son who has emigrated. It was her who forced her son to go away and build a better life. But now she curses foreign lands because she misses him a lot and has realized that nothing can replace his absence.
Searching and discovering treasures of a different “civilization”, “nation” etc. is something that l myself also love, and while you do that with Greek treasures and traditions, you give and take what it is to exchange with these and — simultaneously — we interact within a new, different context.
Sing it now with your lyrics, Patrick!