Symbol, deity, influence: people believe the moon to be many things. This flexibility as a literary or filmic metaphor or motif allows it to be used and re-used again and again. For me, the moon is mysterious but beautiful. She (there's no possibility, for me, of a masculine moon) has subtle power, less direct than the sun, but all the more interesting for it. Contemporary representations tend to be 'spooky' however: a full moon on screen practically always indicates danger to come.
In the Tarot, the Moon card is the Unconscious, the unknown and the unpredictable. For some, it represents falsehood (since we see more clearly by sunlight, the moon is thought to be deceptive), but I cannot square that view, personally - it feels like a relic of more openly misogynistic times when women's wisdom was inherently mistrusted.
Women are related to the moon perhaps because of her liminal nature, waxing and waning, which seems to be mirrored in the lives of human women, most clearly through our menstrual cycle, but also through the longer cycle of girlhood, fertility and post-menopause. Lunar deities, however, are often virginal - e.g. Diana, Artemis - although the moon's phases are also associated with aspects of the wiccan Triple Goddess (maid/waxing moon, mother/full moon, crone/waning and dark moon). Perhaps it is the relative 'coldness' of the moon's light which leads to its association with virginity, especially in the case of the Roman Diana and the Greek Artemis, both of whom are depicted as strongly protective of their single status.
Plath and The Moon
In teaching Sylvia Plath's Ariel collection, I often find myself having interesting discussions with students about the 'meaning' of the moon. For me, "The Moon and the Yew Tree" is a beautiful poem about the failure of the church to satisfy Plath's desire for truth, while the moon, although (or perhaps because?) she is "bald and wild", is ultimately more appealing to her as a symbol. In that poem and elsewhere she associates the moon with her mother, which complicates her use of the symbol, ascribing it negative qualities as well as the 'wildness' which I suspect she admires. It is largely because of this negative association with her mother that some find "The Moon and the Yew Tree"'s moon difficult to read positively. Personally, I think this is symptomatic of the complications of the mother-daughter relationship.
image by Graur Codrin from freedigitalphotos.net