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Yom Kippur, also known as Yom HaKippurim the Torah literally says in reference to,

" Only on the tenth of the seventh month..." (VaYikra 23:27)  

"Only" (אַךְ - ach in Hebrew) teaches that Yom Kippur only atones for those who repent and regret their sins, making every effort to rectify anything they have done.  People who do not repent their sins do not have them forgiven in spite of having lived to this date and beyond it.

The gematria for ach is 21. The Hebrew word for repentance is "teshuvah" which the gematria value of the letters in this word are 400, 300, 6, 2 and 5.  In the minor numerical value (mispar katan) these values are 4,2,6,2, and 5.  This adds up to 20.  If one adds a unit for the entire word, the sum is 21, the same as the word ach.  This teaches that Yom Kippur does not atone without repentance.

When a person repents, it is not enough for him to confess his sins and say, "I have erred, I have sinned, I have rebelled."  He must actually change his ways and stop sinning.

Moreover, simple repentance only helps for sins between man and G-d.  For sins between man and man, Yom Kippur does not help until one reconciles himself with his fellow.


Laws of Yom Kippur

It is a mitzvah to eat and drink a lot on the day before Yom Kippur which is alluded to in VaYikra 23:31:

"You shall afflict yourselves on the ninth of the month" 

The literal meaning of the verse is difficult to understand since we do not fast on the ninth of the month, but on the tenth of the month which is Yom Kippur.  The Torah explicitly said earlier,

"On the tenth day of the seventh month... you shall afflict yourselves" (23:27)

However, the Torah is teaching us that anyone who eats and drinks on the ninth of the month is counted as if he had fasted two days, the ninth and tenth.

G-d loved the Jewish nation so much that He commanded us to fast only one day each year for our own benefit.  He commanded us to eat and drink the day before so that we would have the strength to fast and not be harmed by it.

"This is very much like a king who had an only son.  The king ordered his son to fast, but before the fast he ordered his servants to give the son much food and drink so that he would be able to fast easily."

In addition to its being a mitzvah to eat and drink on the ninth day, it is forbidden to fast on that day.

One reason it is a mitzvah to eat and drink on the day before Yom Kippur is to show that we believe with perfect faith that G-d has set Yom Kippur as a day of atonement and forgiving.  Although we have angered G-d all year, and by rights He should be angry with us for our sins, we have faith that He will close HIs Eyes and forgive us when we repent on this day, and not repay us as we deserve.

There is another reason for eating and drinking the day before Yom Kippur.  Whenever a person keeps a commandment he must do so with joy.  The commandment should not be a burden of which one wants to rid himself.

The commandment to repent is one of the 248 positive commandments of the Torah.  Therefore, according to the law, we should keep it with joy.  However, repentance requires sadness, weeping, and remorse for one's sins.  It is impossible to do this with joy.  Therefore G-d commanded us to eat, drink and be merry on the day before Yom Kippur.  This completes the joy of that commandment.

That is why the eating on the day before Yom Kippur is considered a fast.  It is a preparation for the fast of Yom Kippur.  If one does not behave joyously, then the fast and repentance on Yom Kippur are a little value since they involve grief and suffering.

Eating and drinking have another symbolism.  In the Messianic Age, the Evil Urge (Evil Inclination) will be destroyed and people will no longer sin.  We will then have no need for Yom Kippur.  It will be a day of feasting and rejoicing.  We now do this on the day before Yom Kippur, alluding to our belief in the coming of the Mashiach.

The pre-fast meal (seudah ha-mafseket) should be eaten rather early.  One should then accept the fast upon himself somewhat before twilight (bein ha-shemashot).  This is because one must add some of the weekday to the sanctity of the holy day.

The time that is considered "twilight" is the amount of time it would take for someone to walk three-fourths of a (Hebrew) mile (mil), which is 1500 steps.  Twilight starts a little bit less than one-fourth of an hour before nightfall.

At one-fourth of an hour before nightfall is called Yom Kippur.  If one eats at this time, he may be violating a prohibition for which the penalty is being spiritually cut off.  There is a possibility that this time is considered part of the night.

Moreover, G-d commanded us to add a bit more time; to accept the fast upon ourselves somewhat before this one-fourth hour which is called "twilight.'  Therefore, around one-half hour before night it is considered Yom Kippur even though it is still broad daylight. (Orach Chayim 261)

One must also add a bit of the weekday onto the holy day at the end of Yom Kippur.  It is forbidden to break one's fast or to do any work until it is certain that it is nighttime, when one can see three small stars.  These stars must be in proximity to each other.  If they are far from one another, it is not a true sign of night, and if one violates Yom Kippur, there is a question that he may be violating a prohibition for which the penalty is being spiritually cut off (karet).

If one east the pre-fast meal very early, and there is still enough time, he may eat and drink later as long as he has not accepted the fast upon himself.


Things Forbidden on Yom Kippur

1. Work.  Any work that is forbidden on the Shabbat is also forbidden on Yom Kippur.  The only difference between the Shabbat and Yom Kippur is that is if one purposely does work on the Shabbat, there is a penalty of death by stoning, while if one purposely does work on Yom Kippur, the penalty is being spiritually cut off.  Antyhing that may not be handled on the Shabbat because it is muktzeh may not be handled on Yom Kippur.
2. Eating.  We are forbidden to eat on Yom Kippur. If one eats a piece of food the size of a date on Yom Kippur he incurs the penalty of being spiritually cut off.  This amount, however, is significant only with regard to a penalty.  It is actually forbidden to eat even the smallest amount of food.
3. Drinking. We are forbidden to drink any beverages, including water, on Yom Kippur.  If one drinks a mouthful, he incurs the penalty of karet.  As mentioned earlier, even the smallest amount is forbidden.  The measures only involve penalties.
4. Washing.  We are forbidden to wash on Yom Kippur, whether with hot water or cold water. It is even forbidden to dip one's finger in water.  If one's face, hands or feet or other parts of his body are dirty, he may wash the soiled places.  Thus if one has a nosebleed, one may wash off the blood.  In the morning, one may wash his hands and recite the blessing "Al Netilat Yadayim", ("on washing the hands") as every morning.  However, one must be careful only to wash until the ends of the fingers.  Similarly, if one urinates or defecates, he may wash his hands in the above mentioned manner.  
5. Anointing.  It is forbidden to anoint one's body with anything normally used for anointing.  This is forbidden even if one does not do so for enjoyment, but merely to remove a bad odor.  However, if one does so for healing or if he has scabs on his head, it is permissible.
6. Wearing shoes.  It is forbidden to wear a sandal or shoe made of leather.  It is only permissible to wear shoes made of cloth or other substances. If the shoe is made of wood but covered with leather, it is forbidden.  A woman who is within thirty days after childbirth may wear shoes since cold is dangerous to her health.  Similarly, if one is sick or has a sore or wound on his food, he may wear shoes.
7. Sexual intercourse.  It is forbidden to have sexual intercourse on Yom Kippur.  A man may not touch his wife, just as if she were menstrually impure.

- MeAm Lo'ez; Bachya