パンツの日 means Pantsu Day, a wordplay on the date Aug 2. August -> 8 -> 八 (kanji) -> ハ (katakana), 2 -> two -> ツー, Aug 2 -> ハツー -> パンツ (Pantsu). Note that unlike the pronunciation “pants” suggests, パンツ/pantsu usually refers to underwear in Japanese.

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…

So, like Bunny Day, it’s a day for people to post pics of underwear on Twitter XD.