There’s an accompanying article that covers it, if you prefer reading:
To answer your specific question:
L.A.con II, August 30th - September 3rd, 1984
By the 1980s, costuming at conventions was a pretty regular occurrence: fans would dress up at the annual masquerade or elsewhere. In 1984, a Japanese fan named Nobuyuki Takahashi, ended up attending that year’s WorldCon, LA.Con II in California. He was a fan writer who was there to write about the con for his fellow fans back home, and ended up writing about the masquerade for a local fanzine called My Anime.
As he tried to describe it, he had to figure out the right way to translate the activity that he witnessed. He eventually ended up calling it “Cosplay” — a mashup of “Costume Play". Japanese fans took to the activity enthusiastically, and it’s remained a activity and even vocation there ever since.