This also reveals Hashem’s love for His tzaddikim and the Jewish nation. Hashem had Achashverosh and his entire government move to Persia rather than make Mordechai and Esther move to Bavel! The Rambam (introduction to Pirush HaMishnayos) discusses Hashem’s exceptional care for His tzaddikim. He writes that Hakadosh Baruch Hu can put a desire in a king’s heart to build a beautiful palace because "perhaps the palace was built for a chassid who will stay there one night many years later, and his life will be saved when he stays there." Similarly, Achashverosh moves to Shushan, thinking whatever he was thinking, but it was all for the benefit of Mordechai, Esther, and the Jewish nation.
There are two explanations צחות בדרך as to why this Shabbos is called זכור שבת. One is that Moshe Rabbeinu was born on the 7th of Adar. The custom is to have a shalom zachor on the Shabbos following the birth of a baby boy. As such, this Shabbos was Moshe Rabbeinu's shalom zachor, hence the name Shabbos Zachor.
The Vilna Gaon writes, "This is the meaning of the pasuk, ...אחשורש המלך כשבת בשושן. Achashveirosh was the first king to live in Shushan. All the kings before him didn’t live there... This is recorded in the megillah for us to recognize Hashem's wonders and understand that Hashem prepared every step leading up to the miracle for Bnei Yisrael. Mordechai and Esther lived in Shushan, so Hakadosh Baruch arranged that Achashverosh move his capital there.
The Vilna Gaon adds, “Chazal tell us that one must read the entire megillah, even the seemingly superfluous parts. For example, why is it important to know about Achashverosh’s wealth and power? But every pasuk of the megillah tells us another facet of this great miracle.”
Here's another spectacular miracle, taught by the Alshich HaKadosh, which shows how every detail of the Purim nes occurred with hashgachah pratis: Achashveirosh was awake late at night, thinking how he could reward Mordechai for saving his life years before. Just then, Haman arrived, and Achashveirosh asked him (Esther 6:6) ָרוֹבִּיק ֵץָפח ֶ ךְֶּלַמה ֶרֲׁשא ִׁישבָּא ׂוֹתֲשַעל ַהמ, "What should be done to a man whom the king wishes to honor?" The Alshich points out that Haman came precisely at the right moment for the miracle to occur. Had Haman come a bit earlier, he would have heard from behind the window the reading of the Sefer HaZichronos and would have known that they were discussing the reward Mordechai deserves for saving the king. If he had come a minute later, someone else would have thought about how to reward Mordechai. This shows us Hashem's hashgachah pratis over the most minor detail.
Furthermore, the Malbim zt'l (Esther 2:23) asks why Achashverosh waited to reward Mordechai. Why did he forget to reward him? When Mordechai saved his life, all he did then was write the episode in his Sefer Zichronos. This was so Mordechai would receive the reward at just the right time. Also, let's think about what would have happened if Haman had arrived just one day earlier to request permission to hang Mordechai on the gallows. Achashveirosh would have agreed, knowing Achashveirosh's feelings towards the Yidden. Haman came just at the right day and time so that the miracles could occur.
As we wrote, every word of the megillah reveals miracles. Therefore, if possible, read some commentaries on the Megillah and discover how each word is another facet of the miracle. Let yourself become astounded by the nissim Hashem performs, within the rules of nature, to save His nation, Bnei Yisrael.
Shabbos Zachor is Mesugal for Children
Rebbe Aharon of Belz zt’l told someone who didn’t have children, "Purim Hashem gives mishloach manos, and Hashem’s mishloach manos is children."