Hakushu
There is a significant and demonstrable influcence of Shinto in the philosophy and practice of aikido. One of the most obvious is the practice of bowing and clapping that precedes and closes training sessions in many dojos. As with most rituals, this practice has several layers of potential meaning which may be of interest, to the degree that one is conscious of them. Here are a few thoughts along those lines.
Religious
Traditionally, Shinto includes various rituals the practice of which is meant to align one's own spirit and intention with the spirit of a place. These include kotodama (intoning syllables) and bowing and clapping in the presence of a Kamidana, a small shrine often located in the kamiza, or top position, at the head of a given room.
An aikido practicioner also exploring or practicing Shinto could participate in these rituals to discover what learning might accompany their practice, though the vast majority of aikido practitioners do not identify religiously with Shinto and do not imagine aikido to be a religious practice. Many bow and clap for historical or functional reasons, or without giving the practice much thought, beyond fitting in to the dojo gestalt.
Historical
Morihei Ueshiba, the founder of aikido, was thoroughly versed in Shinto mysticism. He included rituals, religious metaphor, and metaphysics in everyday training, as well as practicing Ōmoto-kyō in a way that shaped his life, his choices, and his art. Many of his students chose to follow him in this, while many others did not.
An aikido practitioner interested in the history of aikido, the metaphors and thinking of the Founder, and in investigating or honoring the traditions valued by sempai (of greater experience/rank) might participate in these rituals to discover what learning accompanies their practice.
Functional
Aiki is practiced as a Do/Tao/Way in many dojos. As with Zen and other systemic practices, one consequence of seeing an applied philosophy as having implications throughout life is the extension of its metaphors to see how they apply to many other areas beyond the literal practice of, for instance, techniques for martial utility. Bowing, especially if one comes from a culture where this is unfamiliar, offers the opportunity to become aware of how one is bowing, how the breath changes, etc. when one is not under many or usual pressures. Sudden noises, claps, striking, can bring one present in a way that disturbs routine and can bring awareness that is indispensible in becoming centered under pressure. Bowing and clapping as part of a group can highlight the ways individuals are aligned and not, how timing requires attention, and many other details which apply in all manner of situations.
Additional Resources
words about Jack Wada's understanding, which I believe also informs Kayla Feder's practice at Aikido of Berkeley