The Rema comments on Shulchan Aruch, Orach Chayim 610:4:
It is customary to dress in clean, white clothes on Yom Kippur, analogous to the ministering angels, and it is customary to wear a kittel which is white and clean, which is also the clothing of the dead (the shroud). Therefore, a person’s heart is humbled and broken.
On the one hand, when a person puts on a kittel or wears white clothing on Yom Kippur, they will become more focused on what the day is about as they contemplate that they are wearing what a person wears when they will one day be buried. This will hopefully put them in the proper mindset to do teshuva.
On the other hand, Yom Kippur is also a happy day. We already see the tradition of wearing white in the mishna (Taanit 26b): Rabbi Shimon ben Gamliel said: Israel had no days as festive as Tu B’Av and Yom Kippur, when the maidens of Jerusalem would go out in white garments that were borrowed…and dance in the vineyards.
The Gemara, Tannit (30b) explains: Yom Kippur is considered an especially festive day since it is a day of forgiveness and pardon and also because it is the day on which the second tablets of the Ten Commandments were given.
On Yom Kippur, we wear white because it is a happy day as we hope that our sins will be forgiven.
In Israel, on Yom Kippur, everyone – religious, traditional, secular – is wearing white. We all stand as equals.
