Translation:The interesting people in the Land of the Youth.
I always understood this to mean "the Land of Youth", not "the Land of the Youth". O'Dónaill agrees with me - he includes "the Land of Youth" as a translation example in the entry for "Tír".
Other dictionaries translate "Tír na Nóg" as "cloud cuckoo land"!
The Land of youth or maybe the land of the young but not the land of the youth. And it is the land of young people of land bestowing eternal youth not the land of A single youth i. E the one who is the object of the sentence rather than youth itself. If you hsve a young child Ireland is the land of the youth but it isnt tir na nÓg
"The Land of the youth" is a strict literal translation of "tír na nóg", because of the way the genetive article works. For example, "the dog's food" is "bia an mhadra", literally "the food of the dog". To put it another way, the literal translation for "tír na nóg" is "the youth's country".
But because "tír na nóg" is a poetic, idiomatic, and literary phrase, we don't translate it literally. Grammatically, "The Land of the Youth" is correct. Idiomatically, is not.
Óg is both an adjective and a noun. As a noun it means a young person or youth. Now go here and you'll see that na nÓg is the plural genitive form of the noun. https://www.teanglann.ie/ga/gram/%c3%b3g
So Tír na nÓg is talking of the people in that land who remain youthful, who are ever young. That should be what is being understood here. And that would be the reason that it was translated as the form I was familiar with Land of the Ever-Young . You're not wrong in understanding it as the land bestowing youth on its inhabitants as a special fountain might bestow youth. In that sense youth is the abstract noun and so it would be óige . And that is another name for the same place, Tír na hÓige where na hÓige is the genitive singular of the abstract noun youth, and this is a direct translation of the Land of Youth. I wouldn't get hung up on exactly how best to give an English translation in this case. I was only really remarking upon there not being an option of the more poetic form we were taught.
Understanding how the meaning changes when you choose óg over óige is more important for us as learners.