As with many of the classical heresies, Arianism emerged from the struggle to reach a consensus on the Trinity. It is named after Arius, whose main concern was that it did not seem fitting that God should have a son. His solution, which became known as Arianism, was to propose that the Son (Jesus) was somewhere between God and man.
"Such is the genuine doctrine of Arius. Using Greek terms, it denies that the Son is of one essence, nature, or substance with God; He is not consubstantial (homoousios) with the Father, and therefore not like Him, or equal in dignity, or co-eternal, or within the real sphere of Deity." 
Modern Arianism shares the ancient belief that Jesus was not (and thus is not) divine, but goes much further reducing Jesus to "just a guy". Influenced perhaps by Naturalism and Materialism, and thus uncomfortable with any supernatural elements, modern Arianism advocates that Jesus was a good and wise man, perhaps even a prophet, but certainly not divine.
It could be argued that such an extreme view has gone beyond heresy to apostasy, thus changing Arianism from a church problem to a mission problem. The views are so widely taught and embraced among liberal churches and seminaries, however, that it is probably unrealistic to dismiss them so easily.
- Rowan Williams, Arius: Heresy and Tradition (Eerdmans, 2002)
- R. P. C. Hanson, The Search for the Christian Doctrine of God: The Arian Controversy, 318 - 381 (T&T Clark, 1998; reprint: Baker Academic and T&T Clark, 2006)
- Arianism (NewAdvent)