When most Heathens and Pagans say "Heathen" today, we mean something far different from the standard dictionary definitions: godless; irreligious; a member of a people of a non-Abrahamic faith (meaning, not Jewish, Christian, or Muslim).
The first definition highly erroneous. We are anything but "godless." Instead, we are, on the whole, polytheistic, with a pantheon of very distinct, individual gods and goddesses.
The second definition varies from person to person; however, most people who identify themselves as Heathen spend a considerable amount of their daily routine discussing, thinking and living their concept of the Heathen way.
The third definition is mostly accurate. While some Heathens do acknowledge the god of the Bible, the majority believe in, and focus on, the deities of our own pantheon and religious constructs... much the same as adherents of any faith do.
So where did this Heathen identity come from? I will frame the discussion somewhat overly simply in order to make it easier to comprehend. During the conversion era, the cities and towns were converted first. The countryside, or the "heath," was converted later. Thus, Christianity was the religion of the city or town dwellers, and the "heathen religion" remained the identity of the rural population... that is, until their later conversion, which was often violent and involuntary.
In short, the origin of Heathen is simply "of the heath" or "of the countryside." In its origins, it does not mean godless, and it does not mean irreligious. We are slowly reassuming control of this identity in English and related languages.
Because "Heathen" is an English word, the "default" meaning for us relates to the pre-Christian religion of the Teutonic peoples (Germans, Scandinavians, Anglo-Saxons, and kindred tribes) and their modern expressions. These modern expressions feature many names, such as Urglaawe, Astaru, Forn Sed, Theodism, Vanatru, and others. These modern denominations share many features but are also divergent, and they also are diverse in their populations.
There are also other forms of Heathenry, including Celtic Heathenry and Slavic Heathenry, and they contain their own identities... and they, too, are anything but "godless."