It's uh, a little complicated and not for polite company. It's shortened from "weeaboo" which you'll probably notice has absolutely nothing to do with anything because it's a nonsense word made up for that one Perry Bible Fellowship strip. At the same time people were being normal on 4chan and making fun of Japan-idolizing dorks with the term "wapanese" and a favorite /b/ modgame was to occasionally add an automatic wordfilter just to stir things up. Well at the bottom of the list there you can see wapanese=weeaboo and that stuck around for a while so the nonsense word picked up a meaning. You still see it written out sometimes but people are lazy so it's usually truncated.

tl;dr it means anime fan and like most web culture of a certain age it's 4chan's fault.