The narrator of The Secret Garden isn't a person, in the sense that it doesn't have a name or a definite point of view. But it does have really strong feelings on what's going on in the novel. Not only does the narrator often tell us directly about the characters—not only what they look like, but also who they are emotionally and morally—but it also clearly lays out its own message for the novel. Consider this excerpt from the first paragraph of the final chapter:
One of the new things people began to find out in the last century was that thoughts—just mere thoughts—are as powerful as electfic batteries—as good for one as sunlight is, or as bad for one as poison. To let a sad thought or a bad one get into your mind is as dangerous as letting a scarlet fever germ get into your body. If you let it stay there after it has got in you may never get over it as long as you live. (27.1)
This is a very strong statement for a narrator with no body, no name, and no explicit personality to make. Essentially, the narrator is laying out the final take-away for The Secret Garden right here: Allow yourself to dwell on sad or bad thoughts, and you'll become as unsociable and accidentally cruel as Archibald Craven. Focus on good thoughts, though, and you'll be filled with "sunlight," like Dickon or Mrs. Sowerby.
The narrator definitely speaks in the third person and is also certainly omniscient (since we get points of view from multiple characters, including Mary, Dickon, the robin, and Archibald himself). At the same time, though, the narrator has its own message that it wants to get across, which it tells us directly as a way to frame and explain the events of The Secret Garden as a whole.