The Tur (693) writes, “Rav Amram z’l writes... to say extra tefillos on Purim since it is a day of miracles (נס יום). We were redeemed from our troubles on this day. Therefore, we must ask compassion from Hashem to redeem us once again.”
The Mareh Yechezkel zt’l teaches that sometimes people daven for things they need, and other times they daven for luxuries. Throughout the year, our tefillos for things we need, such as health, food, and the like, will certainly be answered. However, when we daven for luxuries (such as wealth), it isn’t certain that Hashem will grant our wishes. But on Purim, even our requests for extras are answered. He writes that this is alluded to in the pasuk (Yeshaya 65:24), טרם והיה אענה ואני יקראו, מדברים הם עוד אשמע ואני. The pasuk alludes to two types of tefillos. When one prays for necessities (such as food, clothing, etc.) Hashem says, אענה ואני, “I will answer him and grant his wishes.” However, מדברים הם עוד, when one prays for עוד, extras and luxuries, Hashem says, אשמע ואני, “I will listen.” Hashem listens and considers, but it is not certain that He will grant his requests. Purim is an exception. Even tefillos for extravagances and luxuries are answered. This is hinted at in the pasuk (Esther 9:12), ומה ותעש עוד בקשתך. On Purim even, עוד בקשתך, your requests for extras, ותעש, will be answered.
One Purim, Rebbe Naftali of Ropshitz zt’l was speaking with Rebbe Shalom of Belz zt’l. A simple farmer came by and said to Rebbe Naftali of Ropshitz, “Rebbe, please bless me with a הדיוט ברכת, a blessing of a simple person.” The chassidim laughed (because Rebbe Naftali’s brachos were a צדיק ברכת and not a ברכת הדיוט, a blessing of a regular person). Rebbe Naftali Ropshitzer told them, “Why do you laugh? You didn’t understand what he said. He was asking for the brachos that a הדיוט, a simple person, would ask for. The ovdei Hashem ask for success in Torah, to daven with kavanah and the like. But simple people ask for parnassah. He wants a הדיוט ברכת, a brachah for the matters that a simple person wants.”
The Satmar Rebbe z'tl told this story at his Purim seudah, teaching us that a person should ask for what he truly desires. He shouldn’t be untruthful to himself. If he wants a הדיוט ברכת, that is what he should daven for. After he davens for that, and his heart is already in the process of tefillah, he will ask for spirituality, too.
The Imrei Noam writes, התגברות יש פורים בימי מראש למעלה עד והרצון הרחמים, “On the days of Purim, compassion, and love abound to the highest degrees.” Notice that the Imrei Noam writes פורים ימי, the two days of Purim. This is because Shushan Purim is also a day for tefillah.
The Ateres Tzvi zt’l taught that a person could accomplish more with his tefillos on Shushan Purim than on Purim day.