Translation:The airplane is flying above that forest.
That's actually the one that should make more sense. Hungarian uses postpositions, so the directive marker is behind the noun, unlike in English.
- a fölött - above that
- az erdő fölött - above the forest
Also unlike in English, the demonstratives ez and az are only pronouns, not adjectives. So you can't just say "that forest" like in English, but in Hungarian you need to express it as "that, the forest", essentially doubling this object. That's why you need two postpositions, one for "that" and one for "the forest".
Okay, so in English the demonstratives "this" and "that" can appear in two grammatical flavours. Either as a pronoun, where it works like a noun: "We're in this together." Or as an adjective, modifying another noun: "We're in this situation together."
In Hungarian, there is only the pronoun version, so ez and az cannot attach directly to the noun, but will stay separate. If used together with another noun, it will sound like "We're in this, in the situation, together." That's also why you place the definite article in between in Hungarian: "ez a helyzet", literally "this, the situation". Basically, "a helyzet" describes closer what "ez" is referring to.
And since ez and "a helyzet" are separate entities, they also need their grammatical roles assigned separately, i.e. suffixes and postpositions.
- ez a helyzet - this situation
- ebben a helyzetben - in this situation (lit. "in this, in the situation")
So that's why we get from "az az erdő" to "a fölött az erdő fölött". Both the demonstrative and the forest itself need that position marker, basically making it "above that, above the forest".
You can add the verbal prefix át- to give it a sense of direction.
- A repülőgép az erdő fölött repül. - The plane is currently above the forest.
- A repülőgép az erdő fölött repül át. - The plane is flying over the forest, starting from outside the forest and ending up on the other side.
- A repülőgép az erdő fölé repül. - The plane starts from outside the forest and ends up being above the forest.
The issue here is that "over" often means different things, depending on whether you're talking about a location or a movement. The bridge over the river will always be above the water. But if you say "An aeroplane is flying over the forest", it'll sound like you're describing its route - starting on one side of the forest and landing on the other. That's not what fölött expresses; that's only about the current location, so the less ambiguous "above" is used here.