After Haman was killed, Mordechai went out wearing royal garments, which caused the Jews in Shushan to rejoice. The Megillah records that they had light, gladness, joy, and honor, a well-known pasuk that is said each week as part of havdolah on motzei Shabbos. However, its inclusion is difficult to understand, for this pasuk does not appear to have any connection to Shabbos or havdolah.
Rav Zelik Epstein notes that the Gemara in Megillah (16b) interprets each of these four expressions as a reference to a mitzvah that the Jewish people were now able to safely observe. אורה – “light” refers to Torah, שמחה - “happiness” describes Yom Tov, ששון – “joy” corresponds to bris milah and ויקר – “honor” represents tefillin. The common thread linking these four mitzvos is that they all serve to separate the Jewish people from the other nations of the world.
The Gemara in Sanhedrin (59a) rules that non-Jews are forbidden to engage in learning Torah (except for the laws pertaining to the sheveh mitzvos Bnei Noach). Similarly, non-Jews are proscribed from observing Shabbos (Sanhedrin 58b), and the Yomim Tovim that commemorate the yetzias Mitzrayim are even more unique to the Jews. Bris milah represents a covenant between Hashem and the Jewish people (Bereishis 17:10-11). Lastly, the Gemara in Megillah (16b) says that when the nations of the world see us wearing tefillin, it inspires fear among them as they recognize that the name of Hashem is proclaimed on us.
Because each of the four mitzvos referenced in this pasuk act to differentiate Klal Yisroel, it is quite understandable and appropriate to say it in havdolah, in which we thank Hashem for dividing between: ישראל לעמים - “the Jewish people and the nations of the world”.