旧十六日祭（ジュールクニチー) “Juurukunichii” is January 16th of the Lunar calendar, which is “gusou” 後生（グソー/ グソウ） or あの世、の正月, New Years celebration for the afterlife (the dead). This means another celebration/prayer day for ancestors.
All of the stores have various small snacks for grave offerings, as well alcohol and flowers. Uchikabi (money for the dead in the afterlife) and incense is also burned on this day; the rituals are similar to that of Obon. This morning I saw some people heading out to the graves for this purpose. I suspect mostly only elder people or very traditional families still observe this old custom. I also heard from one of my Okinawan friends that it is usually families who had a death the previous year observe this custom, so perhaps not every family observes it every year.
旧 kyuu: this kanji in front of the date indicates it is a lunar calendar (old calendar) date.
十 juu: ten, 六 roku (ruku in Okinawan): 6 –> so 十六 is 16.
日 nichi: day
あの世 anoyo: afterlife, the “other” world
正月 shougatsu: New Years