The term primal religions often refers to the religions of peoples indigenous to Africa, the Americas, Southeast Asia, and Oceania.
One major aspect of these religions is that they rely heavily on oral tradition. In societies that formed their religious tradition prior to developing a system of writing, oral storytelling is a key component. Whether through song or story, the religious traditions of these societies are passed down through the generations orally.
Another aspect of primal religions is that they are practiced on a local scale. Usually, their practitioners are limited to a small community or group of families. Proselytization is rare, and these religions seldom spread at all beyond their initial followers.
Primal religions are also often polytheistic, meaning they worship many gods. Some gods are certainly ranked higher or lower than others in terms of power, ability, and importance, but there are a pantheon of deities.
Animism is another common component of primal religions. This is the belief that objects and creatures all have a spiritual component. This usually plays out as a respect and reverence for all aspects of the natural world. This even extends to revering a specific location as places can be imbued with a spiritual essence as well.
Shamans are more common in primal religions. These are individuals who serve as intermediaries between ordinary people and the world of the deities and/or the land of the dead. They can serve the role of healer, teacher, and spiritual guide.
Ancestor worship is practiced frequently in primal religions. Since they are usually specific to a small group of families, the religion can serve as a vehicle for remembering and respecting the common ancestors of the community.
There are a number of ways that these religions are reflected in other cultures. Most other religions have intermediaries or guides to assist their practitioners in their religious life. Song and storytelling exist in every culture, even if not used for a religious purpose. Many parts of a culture can derive from a former religious origin even if that is not its purpose today.
In his book, The World's Religions, religion scholar Huston Smith discusses the primal faiths. He describes them as religions practiced by indigenous peoples around the globe, from Native Americans to Australian aborigines.
These faiths all share common characteristics. One is orality: religious stories, beliefs, and rituals are transmitted through word of mouth rather than through sacred written texts, and thus the focus is on the central tenets of the faith, rather than the details.
Second, place is extremely important: the geographic features of a particular area are infused and alive with the divine spirit. This makes it a violation of indigenous religious beliefs, to simply move an indigenous group from one geographic area to another: the religious faith is not portable but is tied to a particular piece of land and its sacred sites. It was, thus, very disruptive, for example, to move Native American groups to reservations in a different part of the country, as happened in the nineteenth-century.
This sense of a god being a god of a particular place would develop into henoism, which is the theological concept that different places are protected by different gods, just as different states in the United States have different governors, and if you cross a state line you are under the jurisdiction of a different government. In henoism, if you moved from your geographic area, your god would no longer protect you.
Third, along with the centrality of orality and place, Smith states that primal religions exist in an eternal now. If religions such as Judaism, Christianity, and Islam have a teleological view—meaning they are looking to a telos or end of history, in which heaven and earth will be joined—that concept of an end is completely alien to primal faiths. Through religious practice, often through a particular rock or stream or other geographic feature, indigenous people connect with the far distant past and distant ancestors as well as the future.
For most indigenous people, there is not a separation between everyday life and religious life (the profane and the sacred), as there is, say, in modern Christianity, where people enter a sacred place on Sunday and then go on the rest of the week with their ordinary lives. For the primal faiths, all of life is bound up in religious rituals.
Since I don't know what culture you are referencing, it is impossible to say how these chief aspects are reflected in "this" culture, but perhaps you could resubmit the question clarifying that—or simply apply these principles to the culture you are considering.