Translation:The one who is Greek is walking beside the taxis.
Again, it's not a very plausible sentence with these words, although the basic structure of the sentence is a common one in Hungarian.
Here's a silly scenario where this sentence makes the small amount of sense that it can make. Several people of different nationalities are doing various things. I see that one of them is walking beside the taxis. I ask you, "Which one is walking beside the taxis?" and you answer, "The one who is Greek is walking beside the taxis."
Maybe it's more helpful to give some similar sentences that are more meaningful.
Az nyer, aki előbb éri el az 50 pontot. (Question: Who wins the game? Answer: That one wins, who reaches 50 points first. Or more coloquially: He who reaches 50 points first, wins.)
Az jön a leggyorsabban az ebédlőbe, aki éhes. (Question: Who comes to the dining room fastest? Answer: That one comes to the dining room fastest, who is hungry. Or more colloquially, He who is hungry comes to the dining room fastest.")
I'm sure others can provide better examples (or correct my mistakes).
Think of "az" as "that one" and "aki" as "who": "That one is walking beside the taxis, who is Greek."
"[Subject] is walking beside the taxis" -- this is the main clause of the Hungarian sentence. "Görög" is just an additional piece of information that differentiates the subject from other people.
A possible translation of your sentence (with "[subject] is Greek" as the main clause): "Az görög, aki a taxik mellett sétál."
I see what you are saying about guilth's translation (which was also my initial one). I'm not crazy about the accepted one, either, though.
Maybe "The one that is walking next to the taxis, who is greek?" It's a little hard to imagine using this sentence, but it's also a little hard for me to imagine using the Hungarian original!
That sentence seems off to me (but I'm not a native English speaker, so I might be wrong here). I'd either use "that one" instead of "the one that" in the first clause (in which case it's a perfect translation), or I would omit "who" (which would make it the reverse again: "Az, aki a taxik mellett sétál, görög.")
Jsiehler's comment here might clear some things up. It also has some meaningful example sentences.
The sentence I suggested is a little off, but possible to imagine using (mainly if one remember halfway through the sentence that one wanted to mention greekness).
I like guilth's sentence, as far as the correct translation of it. (But you're also right that guilth's sentence has translations back to Hungarian that are more correct than the given sentence.)