The date was chosen because, as Robert Kraft noted, it is “the one date we know of from late antiquity on which LXX/OG/Aquila received special attention." Emperor Justinian’s Novella 146 permitted the Jews of the Roman Empire to read the Scriptures in their synagogues in Greek, Latin, or "any other tongue which in any district allows the hearers better to understand the text". Specifically, "We make this proviso that those who use Greek shall use the text of the seventy interpreters..."
I also found a book that I am quite enjoying about the importance of the Septuagint in biblical studies: When God Spoke Greek: The Septuagint and the Making of the Christian Bible, by T.M. Law. So far, it seems to be a very accessible guide. Finally, another great Septuagint resource is Invitation to the Septuagint, by scholars Karen H. Jobes and Moisés Silva.
Have a very happy International Septuagint Day!