In chapter 20 of OP, Hagrid explains that Dumbledore gave to the Gurg a branch of Gubraithian Fire. An enchantment to make it burn evermore. He also says that not many wizards can make it.
What does Gubraithian mean?
Is it similar to the nature of a phoenix?

Gubraithian Fire is mentioned in David Colbert's Magical World of Harry Potter.
He believes the name Gubraithian comes from the Gaelic Language, the phrase 'Alba Gubragh!' means 'Scotland Forever!' and in Irish 'Erin Go Bragh!' means 'Ireland forever!'

It's amasing how many of the terms used by Jk in Harry Potter have subtle connections to language, mythology and legends.

I think you’re probably right about the relationship between the Phoenix and the Gubraithian fire.

Dumbledore seems to have an affinity with Phoenixes; After all his Patronus takes the form of a phoenix.

Maybe you have to have a Phoenix faithful to you to, to be able to perform the charm to make Gubraithian Fire.

Jk mentions in fantastic Beasts and where to find them that "...very few Wizards/Witches ever succeed in domesticating it"

Maybe ‘domesticating’ or getting a Phoenix to respect you is the difficult part in creating Gubraithian Fire.

I think you're correct that the Gubraithian Fire will have some sort of significance in the final two books. J.K. Rowling rarely drops new magical objects and powers into the books for no reason -- the Marauder's Map could have foiled Crouch Jr.'s plans in "Goblet of Fire," the Mirror of Erised had obvious new meaning at the end of "Sorcerer's Stone," even the Polyjuice Potion had significance beyond Hermione's little plot to sneak into the Slytherin common room in "Chamber of Secrets." It would be out of style for her to insert such an enchantment into "Order of the Phoenix" and then let it just sort of die in future plot development.

Unfortunately, I have no idea about what sorts of special powers the fire may possess aside from the fact that it never goes out, and I am at a total loss about how a burning log could affect Harry's quest to conquer Voldemort. When I searched for "Gubraithian" online, I came up with a LOT of Harry Potter fan sites, but nothing else. It doesn't appear in the dictionary or in any encyclopedias either, so I'm pretty sure that it's just something that J.K. Rowling invented. Have we any language experts here who can somehow trace the word back to some Latin root or another?

You're correct that the everlasting quality of the Gubraithian Fire is reminiscent of the phoenix, which obviously lives forever... perhaps there is some link. The phoenix's ability to die and be reborn is only one of its powers, so perhaps there is more to the Gubraithian Fire than we know of as of now (?). It took us several books to get a clear picture of what the phoenix is capable of, so maybe we'll be finding out more about the fire in the future.

I'll continue to think on it..... when would Harry need fire? Hmm...

Good point to draw to our attention!

EDIT: Just saw Souljacker's response... you're way too quick for me! Time for me to crack out all the Harry Potter and mythology reference books, I guess... What could the "Scotland forever" have to do with anything? Unless J.K. Rowling was just feeling like a nationalist while she wrote the book...

*Hehe* I’m always on the search for new topics!

I agree that the Gubraithian Fire having some significance in the next too books, I'm not sure what though!

I don't think the 'Scotland Forever' and 'Ireland forever' have any relevance to the books there just the examples Colbert uses to show how the language can be used in certain phrases.

I think the important thing is the words in the different dialectics of Gaelic for forever; ...Gubragh/Go Bragh...Gubraithian...Forever...

so we get 'forever fire' from 'Gubraithian Fire'.

Wow... I only just understood the 'forever' connection, and I've been looking at your post for several minutes... Gubraithian Fire lasts forever... That was just a tad bit dense on my part! Anyway, that's probably the correct etymology of the word, so one mystery solved. It's really fun how everything in the Harry Potter books has some kind of root in a different language and you can sit around trying to interpret whatever subtext exists related to the word.

I like your idea about having to have a phoenix or something to create the Gubraithian Fire. I wish I owned that "Fantastic Beasts" book... I don't get how I can have three hardcover copies of "Order of the Phoenix" in my house and not own the paperback book, but never mind that. Maybe the phoenix and the fire are symbolic of similar things. I wrote a rather extended treatise on symbolism of the phoenix (click here) back when I had just joined the forums and all of my posts were practically novels. When I take a look at it, it seems that some of my old points fit with the Gubraithian Fire as well, particularly the questions that I ask in the little "Implications" section at the end.

Is there any way to extinguish Gubraithian Fire, do you think? That remains my central question about the phoenix, as well... is it possible to kill one?

Bit of a long way from everlasting fire to Voldemort occupying England and Wales and Dumbledore occupying Scotland and Ireland. Never-the-less, it does seem likely that something from that spell could reappear in a later book.

If the magic phenomenon that constructs the existence of a pheonix and Gubraithian Fire enchantment is the same, then it is fire and immortality.
The pheonix's nature is about faith, hope, loyalty, and love.
Could Gubraithian fire be of the same things?
Is a greater everlasting fire behind the locked door in the Dept. of Mysteries?

I don’t see how a Phoenix could ever be destroyed, after all the Hogwarts Phoenix took an Avada Kedavera and still lived to tell the tale (so to speak)

Maybe the death of a phoenix signifies the end of the world , (kind of like the four horsemen of the apocalypse) as the Phoenix will only die when the world (as we know it) ends.

This could be good news for Dumbledore as he kind of has an affinity with the Phoenix, so maybe he won’t as so many theories have prophesised have to die in order to save Harry.

I think the Gubraithian fire probably exhibits similar properties to the Phoenix. But to be honest while I accept it probably takes an absolutely magnificent bit of magical skill to perform, I can’t see it being of much significance in the second wizards and Witches war. But I suppose it could be, you never know.

well i wish i knew more about Gubrathian fire tell me more

When I first read of the Gubraithian Fire I thought of Prometheus, who stole fire from the gods of Mount Olympus and brought it to men. I'm sure there is alot of symbolism in Hagrid bringing an everburning torch to the Giants, I just don't see how that pertains to the future books, or might give clues to events that have not unfolded.

Perhaps Dumbledore himself meant the torch to be a symbol of his everlasting friendship. Hagrid brought the "light of reason" to the giants, and whenever they see the everburning log they will remember him. That may have been his sole motivation with that particular gift.

His other gifts were an indestructable helm, and a dragon's hide, which, perhaps, symbolize the purpose for which he meant to use them.

Good point Weasel King, I didn't think about that. Wasn't Prometheus eternally punished for giving fire? If it is an echo to HP series, will the bringer of fire be reprimanded as well?
Gubraithian fire reminded me of Moses and the burning bush. That was also a recognition of kinship and an envoy.

I was thinking exactly what Weasel King said

Maybe the punishment for bringing the fire could foreshadow the deathof Hagrid...but thats not for this topic I see.

As for the death of the Pheonix...maybe it dies when it's domesticator dies, and the Gubraithian Fire from that pheonix, if it comes from the pheonix, goes out when the pheonix dies.

Yes, he was cast out to live as a man. I guess that would be eternal punishment. Perhaps that is foreshadowing for Grawp. A sort of twist on the myth. Rather than taking something TO the giants, he took one of them away. I don't know. I don't think a campfire that never goes out would be much use in itself. Might even be dangerous. You wouldn't wanna keep it inside.