Today, the 28th day of Nissan, marks the day that Yericho fell to the Hakafos and Shofar blasts (and not to the military prowess) of B’nei Yisroel. It was none other than Yehoshua Bin Nun who composed Aleinu at that time in recognition of Hashem’s Omnipotence--and the thanks that we owe Him for our position in this world! According to the Sefer Chareidim, as brought in the Siddur Rashban, Aleinu was actually recited forwards and then backwards by Yehoshua and Bnei Yisroel, and this was the final blow that caused the walls to fall in. This Tefillah is so crucial to us that we recite it at the end of each of our daily prayers, and it is the essence of our Tefillos on Rosh Hashanah and Yom Kippur (where we additionally genuflect). The Rema in Shulchan Aruch (Orach Chaim 132:2) writes that we should be careful to recite Aleinu with Kavanah each day.
It is certainly no coincidence--as it never is--that Aleinu was composed so soon after Pesach, as it reflects so many of the lessons to be gleaned from those special days--Thanks to Hashem for choosing us as His People; Awareness of Hashem not only as Creator but in Hashgacha Pratis on a daily basis; Ain Od Milvado…and our longing and prayer for the final Geulah. If you started today to daven Aleinu only from a Siddur, or to be sure to have special Kavannah when reciting it for all of the essential yesodos of Emunah it contains (actually found in the plain meaning of the words), or to make sure that it takes you at least a minute to recite because you are not swallowing the words and you are paying attention to them, bowing down more properly or with thought...or any other improvement--then you will always remember the anniversary of your improvement--the anniversary of Aleinu!