Another wordplay here. In Japanese, 7 can be pronounced as nana (なな), 2 as tsuu (ツー, actually the Japanese transliteration of English pronunciation two), and 5 as go (ご). In a stiff way, the first three syllables of shaved ice (夏氷, なつこおり, natsukoori) is almost the same as 7 (na), 2 (tsu), 5 (go/ko), thus the date July 25 is recognized as the day of shaved ice. Note that this day is set by the Japan Kakigoori Association, not officially recognized by any government institutions.
This summer in Japan has been significantly hotter than previous ones. There have been numerous reports on the high temperature and associated health issues all over Japan. In a hot summer day, a cup of shaved ice would definitely ease the suffering of the 40+ degree Celcius (105+ F) weather. On this Shaved Ice Day, people have a great reason to share on SNS their ice eating experience, which causes the tag to trend on Twitter in Japan.
Interestingly, when I was researching for the day, I found that this day is also Natsuko Day (well, no more explanation needed clearly). Natsuko is a pretty common given name in Japan, and can be written as 夏子, 奈津子, 奈都子, etc. So there is this company officeIKD, which host a concert called 725 meeting (725の会) annualy, that created this Natsuko Day. The first artists to participate in this event are AKAMINE Natsuko (赤嶺奈津子) and YAMAMOTO Natsuko (山本夏子), both Natsukos lol.