The governess and Mrs. Grose are foils for each other. In many ways, they're similar and fairly companionable, but they come from different backgrounds, and their relationship ultimately brings out some of their contrasts. Mrs. Grose, for her part, respects and supports the governess for as long as she can, but she eventually comes to see her as misguided when it turns out that she (Mrs. Grose) can’t actually see the ghost of Miss Jessel:
"She isn't there, little lady, and nobody's there—and you never see nothing, my sweet! How can poor Miss Jessel—when poor Miss Jessel's dead and buried? We know, don't we, love?"—and she appealed, blundering in, to [Flora]. "It's all a mere mistake and a worry and a joke—and we'll go home as fast as we can!"
When Mrs. Grose says she can't see Miss Jessel, she ends up siding with Flora. Until this moment, Mrs. Grose and the governess have formed something of an allegiance, with the governess insisting that Flora is purposefully deceiving them. Now, though, Mrs. Grose effectively abandons her allegiance with the governess.
What's most interesting about this passage isn't just that Mrs. Grose can't see the ghost of Miss Jessel—it's that she speaks very condescendingly to the governess, almost as if she's trying to make her feel crazy. Her appeal to Flora ("We know, don't we, love?") feels especially cruel, since the governess and Mrs. Grose have spent the majority of the narrative as close confidantes engaged in analyzing the children for any sign of something strange or amiss. In fact, the governess even describes their bond at the beginning of Chapter 8 by saying that they are "of a common mind." Now, though, Mrs. Grose immediately appeals to Flora as an ally of sorts, perhaps as a way of defining her own sanity in opposition to what she now sees as the governess's mental instability.
One reason Mrs. Grose might turn so quickly on the governess is that their initial connection is based on more than the mere fact that they're "of a common mind." They are, as the governess puts it at one point, united in the belief that they have a "duty of resistance to extravagant fancies." In other words, they specifically bond over their necessity of keeping their wits about them and resisting any sort of delusional, irrational thinking. And this necessity comes from a sense of responsibility to protect the children. Once Mrs. Grose suspects that the governess isn't thinking clearly, then, the very foundation of their alliance crumbles, and Mrs. Grose begins to suspect that she might have to protect the children from the governess, not from ghosts. Later, though, Mrs. Grose privately claims to believe the governess. And yet, it's unclear if this is really the case, since it stands in direct opposition to what she said at the lake. Either way, the sudden rift in her relationship with the governess establishes them as foils and effectively emphasizes the possibility that the governess isn't of a sound mind.