OK, you've got us – this isn't exactly an image, symbol, or allegory. However, it is a hugely significant word, so bear with us. "Depth" is probably the most notable recurring word that shows up in the story; the Governess is always going on about how she has greater depths, or the children have depths, or how the situation as a whole has depths that are as yet unexplained. We can read this word as a stand-in for the concept of the unknown – or things that are known and hidden, which are even more dangerous.
Mrs. Grose also uses the word to describe her fear of Quint – she's afraid of him, she says, because he "was so clever – he was so deep" (6.10). We're not quite sure what lies in these depths in people, which is what makes them so scary. As you can probably tell, the Governess really loves to know things, so, naturally, things that are unknowable or undiscoverable are menacing to her, and in turn to us, as readers.