Arianism was a major heresy in the early Christian church.  It got its name from one of its proponents, the priest Arius who lived in Egypt in the 3rd and 4th centuries.  Arianism was the belief that Jesus was not really God but was, instead, just a regular (if very unusual) human being.

This heresy was believed in by a few Roman emperors and was especially strong among the Germanic tribes.  If it had become the orthodox position, Christianity would be a very different faith.  There would be no Trinity because Jesus would not seen as a divine being.  This would really not be the same faith as the one that we now know as Christianity.