It says in the Medrash [ב"ר נ"ח] that R' Akiva was teaching his students and they were dozing off and he wanted to wake them up. He said - What did Esther "see" that enabled her to rule over 127 nations? She was the daughter of Sarah who lived 127 years.
How did this idea wake his students up?
It is known that R' Akiva was the foundation of תורה שבעל פה and he thought that his students didn't want to hear from him תורה שבעל פה. Therefore he shows from Esther the truth of תושב"ע. There were 48 Neviim and they didn't add or subtract from the Torah EXCEPT for מקרא מגילה [See Megillah 14a]. This was a revelation of an aspect of תושב"ע [that people added to Torah]. The truth is that Esther went to the king's palace under duress [באונס]. So why did the Gemara ask מה ראתה אסתר למלוך - What did Esther "see" that she ruled ... That implies that she chose this fate?! What this means is that at the beginning she didn't want to go b/c she saw no benefit. Then she saw that the salvation of the Jewish people will emerge and that there will be a revelation of תושב"ע through מקרא מגילה and therefore she went willingly as it says "ותלבש אסתר מלכות" "Esther wore royalty" - meaning that she wore royal clothing willingly. As the Gemara explains: Esther said "כאשר אבדתי אבדתי" - Until now she was intimate w/ Achashveirosh under duress and now it is a willing union. Therefore R' Akiva asked מה ראתה אסתר למלוך על מאה עשרים ושבע מדינות? Implying that she was a willing partner. The answer he gave was that since she was a descendant of Esther who lived 127 years therefore she ruled over 127 countries. In these years she revealed the two aspects of תורה שבכתב and תורה שבעל פה. All of these years were an expression of שני חיי שרה - the "two" lives of Sarah, b/c these revelations lived completely with her. It emerges that all 127 years were a revelation of תושב"ע and thus Esther ruled over 127 countries in order to reveal תושב"ע.
Now we find a concept of separation [הבדלה] in a number of areas. To separate between the holy and the mundane., between the 7th day and the 6 days of work, between the Jews and the nations and between Eretz Yisrael and other countries. The need for separation is b/c on Shabbos there is a revelation of the sparks of Kedusha that are hidden during the six days of the week and Shabbos is מברר ["selects" "clarifies" or "separates"]. It emerges that all 6 days have an aspect of Shabbos in them and the weekdays want to swallow Shabbos up. When Shabbos comes the weekday doesn't have the power to swallow it up. But when Shabbos goes away and has to descend to the mundane world of the weekday and select all the holy sparks of the weekday, at that time the weekday can swallow up the holiness. We make הבדלה in order that the חול shouldn't swallow up the קדושה......
Here is the rest.