Theism refers to a belief in a god or any higher power. Polytheism is a type of theism, it refers to a belief in more than one deity or god. These deities (which are a part of the polytheistic religion) come together to form a Pantheon- which is a group of a particular set of deities present in all polytheistic religions. An example can be seen in the case of Hellenic polytheism or the Ancient Greek Religion, we find that this has 12 Olympic gods who come to form a pantheon, these are Zeus, Hera, Poseidon, Demeter, Athena, Apollo, Artemis, Aphrodite, Ares, Hephaestus, Hermes, Hestia, and Dionysus.
Pantheons usually reflect a tendency to grow over time, either through the formation of a collective, when all the patron deities (deities of various regions come together) or we find the growth through struggle, which results in the subordination of the culture of the previous generations by a new one, as we find in the case of Zeus and his siblings and their struggle to overthrow Cronus who is their father.
These multiple deities are seen as the representation of the various forces of nature e.g. in Hinduism there are five deities for the five elements of the universe namely air (Vayu), fire (Agni), earth (Prithvi), water (Varuna) and space (Indra). Apart from this, the deities may simply be ‘avatars’ of the creator deity -Brahma in the case of Hinduism- or an aspect of the absolute reality.
In such a belief where more than one deity is worshipped, all don’t treat gods equally, like we see in the case of Buddhism that there is a higher goal which is more important to achieve than the worship of the deity, this goal is that of Nirvana or the state of complete happiness. Similarly, we may find that polytheists are Henotheists. This term was popularized by Philologist Max Muller in the 19th century through his work. Henotheism is the practice of worshipping one god while recognizing the presence of the other gods, the god worshipped is often considered to be supreme amongst the pantheon of the deities. This may also be known as monolatry. E.g. Among the Ancient Greek Religion we find that Zeus was the god that has been worshipped as the supreme deity among the pantheon of deities.
Polytheists may also follow Kathenotheism, this term is an extension of the term henotheism and was coined by Max Muller with reference to the Vedas. It refers to it is successive worship of sorts, where the deities are worshipped one at a time, at the same time the existence of the other deities is not neglected. To understand this better once again we can go back to Greek Mythology, where, in the Orphic religion, the orphic hymns address the deities of the pantheon at different times, keep one in mind.
Often the deities and details about their lives and struggles are noted in mythology, here they are shown as being transcendent, in polytheism however one finds that the deities are considered to be closer to human beings, and inhabiting empty spaces in between the worlds
This has been an ancient belief and has been prevalent since the Bronze Age and Iron Age to the development of the Abrahamic Religions (religious communities which claim to have descended from Judaism and are strictly monotheistic) which has been adopted by the Romans in the 4th century. Polytheism lies in contrast of monotheism (belief in a single deity), prevalent mainly in Judaism, Christianity, and Islam.
Hinduism, Shinto (Japanese), Santeria (Afro-American), Neo-Paganism (North Africa, Europe), Confucianism (Chinese), Taoism (East Asia) are some of the prominent polytheistic religions today.