I dunno about the wiki article, but lemme sum it up from what I know.
It’s latin, and it basically means “without wax”. The way that such a phrase evolved into what we consider the meaning of ‘sincere’ is that pottery makers would sometimes use wax to cover up flaws or breaks in the vessels they sold. But those of high quality with no flaws were said to be “without wax” or “sin (san?) cere”. There you go.