Bunny Day is a date pun that occurs on August 2nd or 21st.
"ใใใผ" (banii) looks similar to the numerals ๅ ซไบไธ, which respectively mean 8, 2, and 1. The same pun can also result from goroawase: 8 (ba) + 2 (ni) and 8 (ba) + 2 (ni) + 1 (i).
Some also designate August 23rd as Bunny Day or "Banii-san no Hi" using goroawase: 8 (ba) + 2 (ni) + 1 (i) + 3 (san).