הַבְדָּלָה בְּ״חוֹנֵן הַדָּעַת״: מַאי טַעְמָא
We learned in the mishna that havdala, distinguishing between Shabbat and the weekdays, is added in the blessing of: Who graciously grants knowledge. Here too the Gemara asks: What is the reason that havdala is recited specifically in that blessing?
אָמַר רַב יוֹסֵף: מִתּוֹךְ שֶׁהִיא חָכְמָה, קְבָעוּהָ בְּבִרְכַּת חָכְמָה.
Rav Yosef said: Havdala is recited in that blessing because it requires wisdom to distinguish between two entities, they established it in the blessing of wisdom.
The Gemara teaches us that on Motzei Shabbos we say the Tefila of Ata Chonentanu in the bracha of Chonen Ha’Daas. Ata Chonentenu is referred to as Havdala, as it is with this Tefilla that we declare a separation between Shabbos and weekdays. The Gemara goes on to explain the reason we say Havdala in this Bracha is because Havdala is Chochma and therefore Chazal put it in the bracha for Chochma. Rashi explains that a Chacham knows to discern between that which is ritually pure and that which is impure or between that which is holy and that which is mundane. The Ran (Teshuvot HaGeonim 92) tells us that in fact, Chachma is by definition the ability to discern between two very similar, yet different things.
We find similarly the Yerushalmi (Berachos 5;2) teaches us that if not for Daas, one would not know how to be mavdil, or separate. The Mei HaShiloach (Vol 2 Miketz 4) expounds on this and explains that when one has Yishuv HaDaas, a calm state of mind, one can then discern two seemingly similar things from each other and thereby have the ability to take ideas from other cultures or communities by separating out the good part of it and integrating it into one’s life and leaving the bad behind.
Rav Tzadok (Bo), however, has a different take on this and explains that as Shabbos ends, one feels a spiritual decline as the high of Shabbos fades away. Therefore, one should be mispallel in the Bracha of Daas that the upcoming week should be one which is clean of sin and full of Yirah, like it was on Shabbos. He continues, that we see from the brachos of the Shemoneh Esrei, where we first talk about how Hashem is the source of all. Once we recognize that everything is from Hashem, the ultimate Mavdil, we can then move onto the Bracha of Daas or Chochma and develop a sense of Yiras Hashem, as the pasuk says Reishis Chachma Yiras Hashem. From there we can go on to do Teshuva and experience the Geula Sheleima.