Several heathens have tasked themselves with defining our religion, my favorite of which is the brilliant mind behind the Longship. Blogs from individual, established heathens are incredibly helpful to new heathens. It's a snapshot of someone's life, a personalized toolset to help them uncover the groundwork for their own reconstructionist faith. My goal here is not to explain myself to other heathens, however; this is to help non-heathens and even non-pagans understand what people like me believe.
So, what does it mean when I call myself a "heathen?"
Let's start with the title. The word "heathen" comes from an Old English word, hǣthen, probably best translated to mean something like "country-dweller," and was used to describe people who held pagan beliefs further into the less-developed areas of Germanic Northern Europe. This can be tracked as far West as modern France and as far East as the borders of Russia. It later became synonymous with "non-Christian," and was used in a less endearing tone against those whom the Church could not reconcile with. Now, people who align with these pre-Christian Germanic beliefs have reclaimed the title of "heathen" and use it to describe our religion broadly as Heathenry.
There are a few main beliefs that count as the foundation of heathenry--belief in many gods (polytheism), belief in the spirits of the land and waters (animism), the cycle of gifting, and the World Tree. To get an in-depth description of these concepts, check out the Longship pages on each. I'll give my little summaries here of the parts I want to add information on.
Polytheism. Belief in the gods is fundamental to heathenry. There were many regions that practiced heathenry, such as Norse, Anglo-Saxon, Frankish, Gothic...the list goes on. One hurdle to get past is the modern construct of "pantheons," or forming distinctions between these groups' god beliefs. The borders we see between civilizations simply weren't as apparent to our ancient ancestors. These were travelers, sailors, and traders, constantly exchanging both goods and ideas with other cultures around the world. In fact, I and many other polytheists believe that all the gods exist, we merely choose to or are called to worship specific ones.
Animism. The heathen worldview sees spirits in all things -- from stones to mountains to streams to oceans -- that we refer to as wights or vættir. These beings can be appeased and offended, and their favor dictates the wellness of their domains. In the Viking era, respecting the vættir was of utmost importance. The iconic beast heads at the front of their ships were intended to scare the landvættir of their enemies homelands, driving them from farms and shores and leaving the land barren and weak. The vikings took care to remove these beast heads before going ashore at the rocks of their homes, lest they shoot themselves in the foot.
The Cycle of Gifting. The gods, vættir, and ancestors give us an incredible amount of blessings. They foster our crops, heal our bodies, and strengthen our bonds with our kin. We as human worshipers can aspire to "repay" this debt by offering gifts to them. The point of gifting is not to treat the gods as vending machines for blessings, however--it is critical to continue giving to someone even when you expect nothing in return. Giving to your fellow human does not have to be material. You can give time, love, care, acts of service, and even simple hospitality. Giving to the gods, however, requires a material aspect. The only hope we have of reaching the gods in their unknowable place in the universe is by transmuting the goods we reap on their beautiful Earth. This is completed by offering to them at an altar or shrine, where fire is lit to act as a gateway to the divine. That being said, no god wants their devotees to bankrupt themselves in debt to the divine. Most heathens offer things as simple as salts, herbs, and incense.
The World Tree. Heathen cosmology places humanity squarely in Miðgarðr, one of nine worlds on the branches of the World Tree we call Yggdrasill. These nine worlds house various classes of being that hold power in different spheres, from the chaotic and wild-hearted jötnar of Jötunheimr to the holy gods on their thrones in Ásgarðr. At the base of the tree is a great well of a mystic substance known as Wyrd. The Well of Wyrd is a basin from which our actions' consequences flow to create orlæg, or "first law", for those who come after us. To put it simply, Orlæg is circumstances we are born into, and wyrd is the tapestry of thread that make up potential futures we weave for ourselves, and the ripples that flow from every action we take.
These core ideas are the pillars of my heathenry. Many heathens place priority on different aspects of the religion, but these are ones I felt were necessary to lay out in the open right away.
I know from the outside, paganism may seem like a lot of hippie, new-agey nonsense, but we as heathens actually hold a surprisingly coherent worldview if you just care to look.