Purifying Ourselves Before Pesach
The Gemara Yerushalmi (מגילה פג ה"ה) says that in the midbar the mishkan was first erected on the first day of Nissan, בְּאֶחָד בְּנִיסָן, and on the second day of Nissan, the Parah Adumah's ashes were prepared. This was because the process of preparing the Parah Adumah to be burned had to be performed נֹכַח פְּנֵי אֹהֶל מוֹעֵד, facing the entrance of the mishkan, and later the Beis Hamikdash. Therefore, it could only be done once the mishkan was already erected. According to this the Parshah of Parah should be read during Chodesh Nissan, only after Parshas Hachodesh. The Gemara says that we read it earlier though, because it refers to טָהֳרָתָן שֶׁל יִשְׂרָאֵל the purifying of Yisrael.
Rabbi Tzadok Hakohen of Lublin asks why, now that we unfortunately no longer have a korban pesach, do we not reverse the order of Parshas Parah and Parshas Hachodesh to the way it originally occurred? During the times of the Beis Hamikdash, we read Parshas Parah earlier because we had to ensure that every yid would be pure in order to be able to sacrifice the korban pesach, however that is no longer necessary.
R' Tzadok Hakohen answers that the fact that we still read parshas parah before Chodesh Nissan, indicates that בַּזְּמַן הַזֶּה, we too need to purify our hearts in preparation for korban Pesach. The Kriah of this parsha has the ability to cleanse us of the yetzer hara. Therefore, it precedes Parshas Hachodesh.