The Gemara (Hulin 139b) tells us that Mordechai's name is hinted at in the words "Mor Dror" (Shemot 30:23). This is the name of one of the components of the anointing oil, and Onkeles translates it "Maira Dachia" (which also is very similar to "Mordechai"). According to the Rambam (Hilchot K'lei HaMikdash 1,3; and see also the Ramban's commentary on the aforementioned chapter of the Torah): "The Mor is the blood contained in an animal of India, which people everywhere perfume themselves with." That is, Mor Dror is made of the blood of an impure animal, which is dried and becomes a perfume.   
 

According to this, it appears that the explanation of the Gemara as relates to our subject is that Mordechai's name expresses turning bad into good. And this was really his essence: Mordechai proved that Haman's decree led to good – that as a result of it all the Jews congregated to pray for the annulment of the decree, and indeed their prayer was accepted. And not only was the decree revoked, but additionally the Jews advanced in a number of important ways: 1. Am Israel accepted the Torah willingly (Shabbat 88b). 2. Unity was fostered between them, as the Even Ezra explained that Esther commanded Mordechai to assemble all the Jews to refute Haman's accusation that there was dissention between them – "there is one nation, scattered and divided." 3. B'nei Israel repented, as explained in the Gemara (Sanhedrin 97b): "If they will not repent, will they not be redeemed?  (But) HaShem puts a king over them whose decrees are as harsh as Haman's, and Israel repents and returns to the good path."

One of the components of the Ketoret (incense) in the Chelbenah (galbanum), which has a bad odor when alone, but when it is combined with the other spices of the Ketoret it gives off a pleasant scent (see Drashot HaRan, Drush א). This was also the case with Haman, about whom is said "this evil Haman" but his decrees brought about positive results. And this is hinted at by the fact that the Gematria of המן is the same as that of חלבנה (95).
 

The Midrash says (Bereshis Rabbah, Noach 3): "Rabbi Akiva sat and expounded, and the listeners began to fall asleep. He wanted to wake them up, so he said: "What merit did Esther have that she came rule over seven and twenty and a hundred countries? But (the reason is) that Esther came, who was the daughter of the daughter of Sarah who lived a hundred and twenty seven years, and (thus Esther) ruled over a hundred and twenty seven countries." Certainly, the comparison between Esther and Sarah requires explanation. Rashi wrote at the beginning of his commentary on parshat Chayeii Sarah: "The years of the life of Sarah – all of them were equal for good." And apparently Sarah Imenu had difficult times: she was abducted by Avimelech and Pharaoh, she was barren ninety years, etc. The explanation is that Sarah Imenu had a positive outlook that all is for the good. And so it was with Esther: Despite the many difficulties she went through (being orphaned, being taken to the house of Achashverosh), nevertheless she acted with forthrightness toward HaShem – "she didn't ask for anything" (2:15) and she believed that He, the Blessed One, is the cause of all causes and, and that there was a reason for which she found herself in this situation. And indeed she merited that Israel's salvation came through her. 

The Sages said (Megillah 7b) that on Purim one must drink until he cannot distinguish between cursed Haman and blessed Mordechai. And according to what has been explained, the meaning is that we must attain perfect faith, and accordingly great joy, and through this to recognize that everything HaShem does is for our good. And the purpose of good (which is HaShem's attribute) is to do us good, whether it appears like accursed Haman or like blessed Mordechai.
 

In this spirit we can explain an additional point:
 

The Yalkut Shimoni (Esther 5, 2) asks: "Why is Mordechai called Ish Yehudi (a man of Yehuda)? Because David foresaw that Mordechai would be descended from Shimi ben Gera, and he said: today no man (Ish) of Israel will die. And who is called "Ish"? Mordechai Ish Yehudi. HaShem said to David: You spared Shimi in order that he will beget the Tzaddik. (Therefore) he will be written with your tribe (Yehuda) as it says: Ish Yehudi." It is explained here that Mordechai's existence was by virtue of David HaMelech, and therefore Mordechai is called on his name, "Ish Yehudi." And this is explained similarly in the Gemara (Megilla 12b).

And indeed a number of connections can be found between David HaMelech and Purim:
 

1. David HaMelech was admoni - red-haired (1 Shmuel 17:12). And the Gr"a says that there is a hint in the verse: "ודוד עבדי נשיא להם לעולם" – and My servant David (will be) ruler over them forever (Yechezkel 37:25) – the last letters of these words are מאדי"ם. And in the war against Amalek is said "כִּי יָד עַל כֵּס יָ-הּ" (Shemot 16:17) – the Gematria of "כס י-ה" is 95 like that of מאדים. And also המן in Gematria is מאדים. All of these "coincidences" are HaShem's design.


2. Haman cast his lot in the month of Nissan, since the sign of the month is טלה (lamb), the Gematria of which is 44, the same as דם (blood). In the exodus from Egypt as well, the sign was of blood and slaughter (see Rashi on Shemot 10:10). Am Israel turned this sign to the good through Brit Milah. Therefore Haman decreed that they may not circumcise (Rashi on Megillah 16b). [This was the opposite of Yosef HaTzaddik, who commanded the Egyptians to circumcise themselves (Rashi, Bereshis 41:55) because Yosef is the adversary of Esav (Rashi, Bereshis 30:25) and Esav is the grandfather of Amalek]. In the end – "The Jews had light and joy and elation and honor" and Chazal said: ששון (elation) is Milah (Megillah 16b). Israel continued to practice circumcision, and by merit of this the decree was annulled.

The Tur wrote (Orach Chayim 417) that the three festivals correspond to the holy Patriarchs: "The festivals were established in correspondence to the Patriarchs. Pesach corresponds to Avraham who said (Bereshis 18) 'knead and make cakes' and it was Pesach. Shavuot corresponds to Itzchak, as the shofar sounded at Matan Torah was the shofar from the ram of Itzchak. Succot corresponds to Yaakov, as it is written (Bereshis 34) 'and for his livestock he made Succot.'"
 

According to this, it can be said that David Hamelech corresponds to Purim. Similarly, the Hid"a says that Purim is on י"ד (the 14^th) and this connects it to David HaMelech, since the Gematria of David is 14.
 

We can also find a link in connection with the number of years they lived: the sum of the years of the Patriarchs is 502, the Gematria of בשר (meat) and therefore the primary simcha of the festivals is in meat (Pesachim 109b). David HaMelech lived 70 years – in Gematria יין (wine), as the essence of the Purim feast is wine [and therefore the Purim feast is called "משתה" – a drinking feast, since on Purim drinking takes precedence over eating].

The Torah is compared to meat and wine. The iyun (methodical study) is compared to meat, and the aggadot (narratives) and intellectual enhancements are likened to wine, as the Rambam writes (Hilchot Yesodei HaTorah 4,13): "That one should not stroll in the orchard unless he has filled his belly with bread and meat, and the bread and meat is to know what is forbidden and permitted, and similar (laws) regarding all the mitzvot."  - The primary "food" of the Torah is deep study, and afterwards comes learning the narratives which focus on emotion and on cleaving to HaShem, and this is likened to the wine of Torah. Therefore Purim is the last holiday of the year, since as we know, the three Festivals begin with Pesach.
 

David HaMelech expresses cleaving and singing to HaShem. He composed the Book of Tehillim, the focus of which is love and closeness to HaShem. Therefore the wine is connected to David HaMelech. "And wine gladdens man's heart" – the heart expresses the joy and the elevation above intellect, and "Shira (song) is not said except over wine" (Brachot 35a).
 

And the Megillah says: "And Mordechai would not bow down or prostrate himself." By this, Mordechai expresses unflinching faith that no man can harm his fellow man without receiving permission from above. From where does Mordechai draw this strength?
 

We can explain according to the aforementioned Gemara: David HaMelech acts out of perfect faith that everything is done under Divine leadership and guidance. And consequently, since everything is decreed from above, including the actions men do out of their choice, David does not put Shimi to death, but says: "Leave him and he will curse, for HaShem has told him (2 Shmuel 16:11). This conviction was passed down to Mordechai the Jew, and he, as well as Esther, would regularly say and teach His flock: "All that the Merciful One does, He does it for the good (Brachot 60b)."
 

May we merit to fortify ourselves with complete faith in HaShem and His leadership of the world, and to eternal redemption in the month which was transformed from grief to joy and from mourning to a festival, Amen.

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