One who follows an ancient polytheistic or pantheistic religion and therefore does not follow one of the World's main religions, especially if such follower is not a Christian, Muslim, or Jew.
Paganism is an umbrella term for a variety of religions, both historical and contemporary. The vast majority of these religions (but not all) are polytheistic to some degree. They also tend toward being orthopraxic rather than orthodoxic that is, they place more emphasis on correct action (performing rituals, etc.) than they do on correct belief (most forms of Paganism leave room for a variety of actual beliefs about the divine). Modern Pagan religions are best understood as those which revive, reconstruct, make reference to, and/or are inspired by the non-Jewish, pre-Christian, and pre-Muslim religions of Europe and the Middle East. ("Paganism," due to both its broadness and strongly European connotation, is not a good term for Eastern religions such as Hinduism or Shinto, or worldwide indigenous religions. It is for this reason that followers of African polytheisms prefer the terms "African Traditional Religions" or "African Diaspora Religions," as it gets the point across without shoving these systems into European paradigms.) Some examples of modern Pagan religions include Wicca, other religious witchcraft systems, Neo-Druidry, Asatru, Hellenic polytheism, Religio Romana, Kemeticism (Egyptian Paganism), Celtic revivalism/reconstruction, Romuva, Slavic reconstructionism, and many others.
There is a persistent meme in the modern Pagan community that "all Pagan religions are earth-based," but this is untrue. The civic religions of ancient Athens or Rome (and modern reconstructions of these), for example, are no more earth-based than Christianity. The prominence of the modern Pagan religion of Wicca -- a genuinely earth-based tradition of religious witchcraft founded in England in the 1940s by Gerald Gardner has, unfortunately, led to the belief that all Pagan religions are just variations on Wicca, which is incorrect. Pagan religions such as Hellenic revivalism/reconstructionism followed very different historical paths of development, and have very different focuses. It also diminishes the usefulness of the term "earth-based," which is best reserved for religions like Wicca, Druidry, and several others for which reverence for nature is a central defining feature of the religion; while most religions that existed prior to the Industrial Revolution (including Christianity) had prayers and festivals for good harvests, etc., not all of these religions conceptualized the natural world as the primary focus of their religious energy.
For further discussion of definitions of Paganism, see the Pagan Primer at the useful, and multi-faith, Pagan site The Cauldron: A Pagan Forum.