The story
Blend of popular + furry. Attested as early as 2007 (see quotations), but popularised by a 2009 musical comedy sketch at the Furry Night Live variety show of the Further Confusion furry convention that used popufur as a synonym for popular. Compare similar terms like horse famous (“influential or famous within the brony fandom subculture”).
Etymology from Wiktionary, CC BY-SA 4.0.