Mrs Moore acts as a bridge between East and West without even knowing it. While other characters make judgements and divisions according to race, colour, and creed, Mrs Moore looks to make simple connections with other people. Her first meeting with Aziz in the mosque amply demonstrates this, when she talks to him simply and easily regardless of all the racial, social and cultural differences between them.
Other people among the English, most notably Fielding and Adela, also want to reach out to the Indians, but not quite on the same instinctual level as Mrs Moore. Fielding and particularly Adela engage in long intellectual discussions, but Mrs Moore doesn't. She has no need to rationalise what she does; she simply does it. She does not make a big deal of ‘seeing India’ as Adela does, rather she reacts to Indians simply as people, and espouses a simple religious/spiritual creed of unity. Adela remarks on her complete lack of pretension:
While we talk about seeing the real India, she goes and sees it, then forgets she's seen it. (chapter 3)
The sense of Mrs Moore's essential goodness does impress other people; both Aziz and Adela claim lifelong friendship with her, although she does nothing for them in practical terms (does not help out Aziz at the trial, for instance). Her breakdown, when faced with the apparent emptiness at the heart of all things in the caves, is disturbing. She eventually comes to function more as a symbolic rather than a literal character - transmuted, perhaps grotesquely, into a Hindu Goddess: ‘Essmiss Esmoor’ (chapter 24).
Mrs Moore's role in the novel, then, is to show what people can be like when they set aside all the relatively superficial distinctions made on the basis of race, culture, religion, age and gender. It might be said that she represents the essence of humanity. Her fate also shows, however, that even such innocence can be challenged and eventually overwhelmed by the complexities of life, society, and the universe.