Done for love, and not for money. Amateur is the ideal for fannish activities.
When some money is involved (for example, in the case of fanzines available for "the usual"), it is still amateur if money is not a significant part of the motivation for the activity. (Note that we're talking motivation, and not actual reality: A magazine which is intended to be a money maker doesn't become amateur just because it fails to attract subscribers. Likewise, a convention which consistently makes money can still be amateur if the people working on it do not do so to personally make money.)