All Jewish days begin at night and end at night. Since it is unclear whether that should be at sunset or when the stars come out, for Biblical practices we take the more stringent approach. Therefore, even though Yom Kippur begins before sunset,
it ends the next day after the stars come out. Thus, the Holiday lasts about 25 or so hours (depending on where you live, and other factors).
The time of stars coming out means the time when you should be able to see three medium-sized stars in the sky (that is, the time that you would be able to see them where there is no light pollution and where there are no clouds to block out their visibility).
The night after Yom Kippur ends is called «Motza Yom Kippur,» which means «the exiting of Yom Kippur.» This is the standard term used, as in Motza Shabbos (Saturday night after the Sabbath ends), or Motza Yom Tov (at night after a Jewish Holiday has ended).
After Yom Kippur ends, we must say Havdalah, the «Separation Recital,» before we may eat or do much of anything. In those synagogues where they say Havdalah in the synagogue after Shabbos ends, they should do the same thing after Yom Kippur ends.
Havdalah is said over a goblet of wine, as usual. However, we do not say the usual Brachah (Blessing) over b’somim, the sweet-smelling spices or leaves, and we do not smell them. (1)
However, we do say the Brachah over the torch, as is usually said during Havdalah after Shabbos. (2) This is unlike Havdalah after every other Yom Tov (Jewish Holiday), when we say the entire Havdalah but omit the blessing over the torch.
Furthermore, on Motza Yom Kippur, unlike Motza Shabbos, we may say the brachah for the torch only over fire that has been burning the entire Yom Kippur. We do not light a new fire for this brachah in Havdalah. (3)
This begs several questions. One, why must we use a fire that has been burning since before Yom Kippur, and why may we not light a new one? Secondly, why do we say this brachah over a torch after Yom Kippur, when we don’t say it during Havdalah after any other Yom Tov? Doesn’t it belong to the ending of Shabbos?
In order to answer these two questions, let us examine the reasons for saying this brachah at both these times, Motza Shabbos, and Motza Yom Kippur.
The reason that we say the Brachah over a torch on Motza Shabbos is because Motza Shabbos was the very first time that humanity ever experienced fire.
Adam and Eve sinned on the very first day they were created, Erev Shabbos (the day before Shabbos, i.e., the first Friday). According to the Midrash of Pirkei D’Rebbi Eliezer, Hashem allowed them to stay in Eden over Shabbos. They were expelled from Eden on Motza Shabbos.
That was the first time they ever experienced the dark and cold. At that time, Hashem had mercy on them, and taught them how to make fire. They had never needed it before. Adam, coached by Hashem, took two stones, and made a fire. Adam then thanked Hashem for this. This took place on the very first Motza Shabbos after Creation. Therefore, every Motza Shabbos, we thank Hashem for the creation of fire.
Now, that does not apply on Motza Yom Kippur, since fire was not first given to humanity on Motza Yom Kippur.
On Motza Yom Kippur, the reason for saying that brachah is very different. We are actually saying this Brachah to show that manipulating fire was forbidden during that day, and is now permitted. This is a very different reason than the reason for saying it on Motza Shabbos. (Manipulating fire is forbidden on Shabbos or on Yom Kippur. During every (4)Yom Tov except Yom Kippur it is forbidden to create or extinguish fire, but it is permitted to manipulate and use fire.)
Now, in order to show that it was forbidden to move fire during Yom Kippur, and now it is permitted to move it, we must use fire that was actually burning during Yom Kippur. We show that this fire existed, but we refrained from moving it or manipulating it in any way the entire Yom Kippur, and now, Motza Yom Kippur, we are using it, since it is permitted. That’s the reason for saying this brachah on Motza Yom Kippur.
Therefore, in order to say the Brachah on the torch on Motza Yom Kippur, we must use a fire that has been burning all Yom Tov. Therefore, before Yom Tov, we light a 26-hour (or longer) candle, and let it burn the entire Yom Kippur. After Yom Kippur, we take from that fire to light the torch.
On a regular Motza Shabbos, on the other hand, we may use a new fire (or an existing one, if you wish), because, after all, Adam himself made a new fire and thanked Hashem for it. But on Motza Yom Kippur, we must take from a fire that has been burning all Yom Tov.
The night after Yom Kippur is a time of joy, and a minor Jewish Holiday. (5) We eat a Yom Tov (Holiday) meal, and we rejoice. (It is suggested not to go directly from fasting to eating a major meal, but to eat a few light things, wait a while, and then eat a real meal.)
The reason that Motza Yom Kippur is a minor Yom Tov is because Hashem has promised us that if we repent and pray on Yom Kippur, our sins will be forgiven. Therefore, says the Midrash, when we leave the synagogue on Motza Yom Kippur a voice in Heaven calls out the verse in Ecclesiastes (6), «Go, eat your bread with joy and drink your wine with gladness, for Hashem has already approved your deeds.» (7)
Those who are careful about the Mitzvos try, if they are able, to start building their Sukkah on Motza Yom Kippur (after eating), in order to move immediately from one Mitzvah to another Mitzvah. My late father, of blessed memory, used to nail up one board in place, just to get it started.
One should preferably try and finish the rest of the Sukkah the next day, if possible. (8) The reason cited there is that if a Mitzvah comes your way, you should not let it get old, but do it immediately.
Motza Yom Kippur is a transition into the Holiday of Sukkos, which is a period of joy, since we know that we have been forgiven.