A distinct and unique cast of light shines upon each Holy Day that sets it apart from the others on a spiritual level; and each Holy Day likewise commemorates an important event that sets it apart historically too, as we’d seen (see 4:7:6). We’re thus enjoined to read-out special selections from the Torah each Holy Day that touch upon all that — aside from the regular Torah readings we do on Shabbat and on certain weekdays.
For we’re to read-out from the Torah on a regular basis because it was granted to us to be studied both publicly and privately, and to thus be made an integral part of our lives; and we also read it out so as to be nourished by its great light (see 4:2:2). So we recite the relevant readings on the Holy Days to bolster our connection to the Torah, to bask in the light that irradiates from the words, and to recapture the spirit of the days involved.
And so on Passover we read about the events surrounding the redemption, on Shavuot we recount the granting of the Torah, on Sukkot we retell how we’d lived in booths on the way to the Land of Israel, and the like.