In Japanese, the term is 大樹根. Now, i can see why the translators translated it in "Great tree": if you take the kanjis separately, it comes out 大 ("big, great"), 樹 ("tree") and 根 ("root"), therefore it sounds pretty logical to translate this as "roots of the Great Tree". Unfortunately, they didn't know that Miyazaki's writing style is made of play-words and, most of all, ancient kanji. In fact, 樹 and 根 must not separated, but they are part of one single term: it's not 樹 and 根, but 樹根... which means "root".
樹根 is an ancient term used in times when Kanjis just got exported in Japan from China, and therefore still holds the same Chinese meaning, which is "root". Poor translators couldn't see this little detail, even if it's not the first time Miyazaki uses pretty ancient terms often related to Japanese (for example, Chaos in Dark Souls is 混沌, which is related to Chinese mythology).