Third-person omniscient? Sounds fancy, but English teachers often use fancy words to make simple things look all sparkly and expensive. The idea of third-person omniscient is pretty commonplace. In fact, you've probably already experienced it many times beforehand.
When your teacher says a story is written in third-person, it means the story isn't being told by a character inside the story. Instead, the narrator is an outside observer, someone looking in. More often than not, you can tell this technique by the pronouns the narrator uses. If the narrator uses pronouns "he" and "she" to refer to the focal character, then we can safely call it a third-person narration (as opposed to first-person narration). In Dune, the narrator isn't inside the story but someone outside telling us about Paul Atreides and his adventure—so it's third-person.
But what's this omniscient business? Well, an omniscient narrator is one who can occupy multiple characters' points-of-view, giving the reader access to anyone's thoughts, feelings, and actions at any time. In Dune, the narrator slips between multiple characters' POV on the fly. For example, in chapter 15, we start in Kynes's POV and get his thoughts:
I will have Stilgar send Idaho's head to this Duke, Kynes told himself. (15.15)
Then the narrator moves on to give us Duke Leto's actions from his POV:
As he approached the solitary figure near the ornithopter, Leto had studied [Kynes]: tall, thin, dressed for the desert in loose robe, stillsuit, and low boots. (15.18)
Clearly, Kynes isn't studying himself, so we know a switch has occurred. Finally, we jump over to Paul's POV:
Paul nodded, impressed by [Kynes's] air of strength. (15.25).
In just ten paragraphs, we enter the minds of three characters! If this were third-person limited, the whole scene would have to play out from one or two characters' POV. Since that's clearly not the case, we can safely check third-person omniscient as Dune's narrative technique of choice.