This might be easier to understand in a full sentence. One could be:
Az az a férfi, aki az asztal mögött áll - That is the man who stands behind the table.
"az a férfi" is just "that man" in English. There's no implication of "is" in the Hungarian sentence.
Aki is a relative pronoun. You must have seen it elsewhere in your studies. It's like the use of que/che in Spanish, Italian French, что/кто/который in Russian.
I really wish they would change this to use full sentences. It would make it alot easier to use ami and aki.
This is really awkward in English - it would only ever be a clause of a longer sentence.
I have no clue why they say this sentence implies "she". Im hungarian and know it pretty well.
Why is "that stands behind the table" not accepted?
A bicikli, aki (edit: ami!/e) az asztal mögött áll, piros. The bike, that stands behind the table, is red. Or is there anthing wrong with that?