Our Gemara on Amud Beis discusses what most commentaries believe serves as the basis for the custom of the Kol Nidre service on Yom Kippur.  There are numerous kabbalistic theories as to what it signifies. On the most basic level, a person wants to come into the Day of Judgement clean and clear of any unfulfilled commitments.  On a deeper level, annulling vows publicly may inspire a theurgic heavenly response of releasing and forgiving sins and decrees (See Psychology of the Daf, Rosh Hashana 29, where we discuss the power of symbolic actions in prayer.)  Some say the custom of Kol Nidre originated with the marranos, who on the Day of Judgment, sought forgiveness and amnesty for vowing fealty to Christian beliefs.

However, I would like to add a new thought to explain this custom.  The Gemara Bava Basra (120b) tells us that the process of annulment of vows is relatively unique in halacha.  While ordinarily, one should not use a Beis Din (Jewish Court) composed of plain Jews, who are not trained to be judges to adjudicate, for annulment of vows, even non-dayanim can serve, see Rashbam Op. Cit.). Of course we all experience this when we do Hataras Nedarim in Shul on Erev Rosh Hashana, and most of us are not trained dayyanim.

I believe the message is, that on this holiest of days, where we say (Rosh Hashana 18a):

״דִּרְשׁוּ ה׳ בְּהִמָּצְאוֹ״…“Seek the Lord while He may be found; call upon Him when He is near” (Isaiah 55:6), 

אֵימַת? אָמַר רַבָּה בַּר אֲבוּהּ: אֵלּוּ עֲשָׂרָה יָמִים שֶׁבֵּין רֹאשׁ הַשָּׁנָה לְיוֹם הַכִּפּוּרִים.

When is God near to him? Rabba bar Avuh said, These are the ten days between Rosh HaShana and Yom Kippur. 

On this day, all Jews can be equal before Hashem.

Perhaps this is also why we recite in the Kol Nidre liturgy:

עַל דַּֽעַת הַמָּקוֹם וְעַל דַּֽעַת הַקָּהָל. בִּישִׁיבָה שֶׁל מַֽעְלָה וּבִישִׁיבָה שֶׁל מַֽטָּה. אָֽנוּ מַתִּירִין לְהִתְפַּלֵּל עִם הָעֲבַרְיָנִים:

With the consent of the Almighty, and consent of this congregation, in a convocation of the heavenly court, and a convocation of the lower court, the court of man we hereby grant permission to pray with transgressors.