Polytheism's basic premise is that individuals can worship different examples of divinity to represent the divergent nature of being in the world. For example, the Greeks felt that different endeavors compelled one to worship different gods, paying deference to all. For example, Apollo was seen as a god of medicine while Artemis, the goddess of the hunt. For each endeavor, one needed to pay the required deference to the specific deity. One could not afford to neglect the other deities, but in needing the benevolence of the gods for a particular task (health, being a doctor, or commencing a successful hunt), one needed to pay deference to that particular deity.
In more contemporary settings, a polytheistic setting understands the different gods and goddesses as a reflection of a universal essence. To pray to one of them for a particular element reflects a way in which human beings can honor a specific example of that transcendental and universal essence in a specific way. For example, if one prays to the Mariamman Goddess in Samayapuram, India for healing of a specific health ailment, it is a specific expression of the universal essence. Human beings are able to channel their own feelings of fear and insecurity to a particular form of the divine. Polytheism thus allows for an individualized and specific expression of what it means to be human and subjective in an objective manner. It is both specific and universal, all at once. It is here where I think that polytheism becomes so meaningful to so many as it seeks to bridge the gulf between the individualized context and the universalized one.