Bunny Day is a date pun that occurs on August 2nd or 21st.
"バニー" (banii) looks similar to the numerals 八二一, 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).