The Ibn Ezra writes that this is simply a long time to fast, which demonstrated the Jews’ renewed loyalty to H-Shem.
R’ Yehonason Eibshutz writes that Esther mentions both night and day because days and nights added together equal six regular, Halachic days. This is the amount of time the Jews spent at the seven day feast of Achashverosh (see 1:5) because they were not there for Shabbos.
The Ohel Moshe quotes R’ Yosef Rozofsky that three full days of fasting naturally affect a person’s grace and beauty, which are the characteristics Achashverosh saw in Esther. This is why Esther only fasted for 70 hours, instead of three full days.
The Ben Ish Chai writes that night and day represent different kinds of Torah. The Torah one learns at night should be Oral and the Torah one learns in the day should be from the Written Torah, TaNaCh. Esther’s stressing both of these times means that she wants the Jews to learn both kinds of Torah to gain a closer relationship with H-Shem.
Perhaps she mentions night first because, historically, the Oral Law begins shortly after this period. Megillas Esther is full of hidden miracles, which are flushed out through concentrated, deliberate thought – the very essence of Oral Law.