• ... the day of 利休忌, rikyuu-ki, an annual (Buddhist) memorial service for Sen no Riykuu. And if you don't know who Sen no Rikyuu is, clearly you haven't spent enough time kneeling in front of exquisitely rustic pottery.

  Except, actually, 利休忌 is only today in the Omotesenke (表千家) tea ceremony tradition. The Urasenke (裏千家) folks observe 利休忌 on the 28th. And Rikyuu himself actually died on April 21st. I have no idea what that's all about.

• ... さくらの日, sakura no hi, Sakura Day. The sakura start to blossom around the end of March (depending on where you are), but why the 27th specifically? It's a mathematical pun. The word for "blossom" in Japanese is sa-ku, and if you put it into short-form numbers [a whooole other post, that], that's 3-9. 3 x 9 = 27. Groan.

• ... 仏壇の日, butsudan no hi, Buddhist Altar Day. This commemorates an order given by Emperor Temmu in 686: 「諸国の家毎に仏舎を作り乃ち仏像及び経を置き、以て礼拝供養せよ」 ("Let a Buddhist place of worship be built in every home in every province; furthermore let Buddhist statues and sutras be placed therein; this having been done, pray and remember the dead there"). Those butsudan are still in most Japanese homes today.
  

Today's events come courtesy not of Wikipedia but rather of this page, which although barely legible is quite informative.