バニーの日 means Bunny Day, a wordplay on the date Aug 2. August -> 8 -> 八 (kanji) -> ハ (katakana), 2 -> に, Aug 2 -> ハに -> バニー (Japanese for Bunny).

Like mentioned here,

On SNS in Japan, there are numerous cases of such wordplay. They are somewhat netizen-made festivals when SNS users use as a reason to post about the topic…

It’s worth mentioning that bunny is a popular theme of otaku culture (probably imported from the west). There is this special category of outfit called bunny girl.