The mitzvah of eating on Erev Yom Kippur at first glance presents an enigma. The festive nature of the meal seems to contradict the serious mood of the next day which is filled with beseeching, pleading, and multiple confessions repeated ten times in five separate t'filot.
Rabbeinu Yona (Sha'arei T'shuva 4:8) offers three explanations for this meal. First, a person expresses joy anticipating the day when his sins will be forgiven. This joy indicates a person's concern about his sins and their effects and his yearning for them to be removed. Second, just as a festive meal is served on Yom Tov, so too we have a festive meal on Erev Yom Kippur reflecting the joy of Yom Kippur. This meal cannot take place on Yom Kippur because of the obligation to fast so it takes place a day earlier. Third, we prepare for the service of the day to pray and confess our sins by strengthening ourselves beforehand by partaking of a meal. Much discussion as to the halachic ramifications of these three reasons appears in poskim. [See Moa'dim b'Halacha for an overview.]
This meal further demonstrates a dual theme begun on Rosh HaShana. On the one hand, the Shofar blasts instill a sense of dread and awe; in the language of Rambam, the Shofar calls out "Awaken O you slumberers and examine your deeds!" On the other hand, we partake of festive meals in accordance with the passage in Ezra "go and eat savory foods … for the joy of G-d is your stronghold!" (Nechemia 8:10). So too on Yom Kippur, the climax of the Ten Days of Repentance, we are filled with dread at the final day of the "sealing of the Judgment" of Rosh HaShana, the day when the beinonim will be judged if their repentance merits their being inscribed in the "Book of Life". But on the other hand, in the language of Rabbi Akiva (Yoma 8:10), "praiseworthy are you, Israel, before Whom are you purified and Who purifies you? your Father in Heaven! … Hashem is the mikveh of Israel. Just as a mikveh purifies the impure, so too the Holy One Blessed Be He, purifies Israel." Rabbeinu Yona's first reason especially highlights these seemingly contradictory themes. We are happy, says Rabbeinu Yona, for the opportunity to have our sins forgiven. But this very happiness "serves as testimony about his worry over his sin, and his sorrow over his iniquities."
"V'gilu bir'ada" (Tehillim 2) and be joyful with trembling is an oft-quoted verse expressing this commonly occurring duality of fear and love, trembling and joy (see B'rachot 30b). It is especially relevant for Yom HaKippurim, a day suffused with Hashem's Divine Presence, the mikveh referenced by R. Akiva causing the purification from sin as explained by many commentaries. Being in the presence of the Divine is frightening but uplifting, paralyzing but gladdening. The same dual sense of awe overcoming the Kohein Gadol entering the kodesh kadashim with the incense - clearly accompanied by his joy of serving as the agent of achieving atonement for the sins of Israel - guides us in our synagogues, our mikd'shei m'at (minor sanctuaries), on this unique day. Rav Y. D. Soloveitchik zt"l suggests that the vidui (confession) on Yom Kippur serves not in the classic role of the vidui of t'shuva but as a vidui on a korban. The one bringing the korban must lean his hands on it and mention the sin for which it was brought. This is in addition to the vidui and t'shuva process already begun before bringing the offering. So too on Yom Kippur, the t'shuva process was already to have begun before Yom Kippur. We recite vidui on the vehicle of atonement which is the Day of Atonement itself. Chassidic masters would only refer to this day as Yom HaKadosh. The Talmud calls it Yoma, "the Day". Its holiness and mystery not surprisingly fill us each year with the sense of "gilu bir'ada!" May we merit with our t'shuva and our confession the dual promise of kappara and tahara, atonement and purification, "Ki vayom hazeh y'chapeir aleichem l'taheir eschem mikol chatoseichem, lifnei Hashem titharu!"