"AND FOR EVERYTHING, G-D OF FORGIVENESS, FORGIVE US, PARDON US, ATONE FOR US" (from the "Al Chait" prayer)
Excerpted and Translated from the the Teachings of Rabbi Gershon Steinberg ztz"l
L'ilui Neshamat HaGaon HaTzaddik R' Gershon Avigdor Ben Chaim ztz"l
L'ilui Neshamat R' Yochanan Yitzchak Ben Nachum z"l
L'ilui Neshamat Yaakov Ben Matisyahu HaLevi z"l
L'ilui Neshamat Michael Ben Nachman z"l
L'ilui Neshamat Zehava Bat Shlomo z"l
L'ilui Neshamat Esther Mushka Bat Yaakov HaLevi z"l
L'refuat Hanefesh V'l'refuat Haguf L'Malka Bat Rivkah Zlata
L'refuat Hanefesh V'l'refuat Haguf L'Deena Bat Tzion Bat Zehava
L'refuat Hanefesh V'l'refuat Haguf L'Chaya Basha Bat Esther
L'refuat Hanefesh V'lrefuat Haguf L'Etan Naphtali Ben Zehava
L'refuat Hanefesh V'l'refuat Haguf L'Rivkah Goldah Bat Chaya Basha
L'refuat Hanefesh V'l'refuat Haguf L'Shimon Ben Rivkah Goldah
L'refuat Hanefesh V'l'refuat Haguf L'Yoledet Simcha Pearl Bat Rivkah Goldah
L'refuat Hanefesh V'l'refuat Haguf L'Ahuva Nechama Bat Simcha Pearl
L'refuat Hanefesh V'l'refuat Haguf L'Moshe Shlomo Ben Rivkah Goldah
L'refuat Hanefesh V'l'refuat Haguf L'Chaim Sh'muel Ben Rivkah Goldah
L'refuat Hanefesh V'l'refuat Haguf L'Avital Bat Rut
L'refuat Hanefesh V'l'refuat Haguf L'Eliezer Yitzchak Ben Bracha Devorah
L'refuat Hanefesh V'l'refuat Haguf L'Michael Itzhak Nesshael Ben Avital
L'refuat Hanefesh V'l'refuat Haguf L'Naomi Chana Bat Chaya Basha
L'refuat Hanefesh V'l'refuat Haguf L'Refael Ben Masha Etel
L'refuat Hanefesh V'lrefuat Haguf L'Fruma Freidel Bat Esther
L'refuat Hanefesh V'l'refuat Haguf L'Rav Daniel Reuven Ben Esther and
L'refuat Hanefesh V'l'refuat Haguf L'kol Am Yisrael V'l'geulah Hashleima Bekarov
"...Seal the mouths of our adversaries and accusers..." (from the "Avinu Malkeinu" prayer)
The Chafetz Chaim says that when a man requests "...Seal the mouths of our adversaries and accusers", he is asked in the Upper Realms: "What about your mouth? Do you guard your mouth?", but when a man is careful about his speech, then his prayer is accepted.
It's a Mitzvah to eat on Erev Yom Kippur, the day before Yom Kippur.
There are several reasons for this. There are those that say that it is in order for a person to have the strength to fast. And there are those that say the reason is that on every Holy Day, half of the day needs to be for Hashem, and that is the prayer, and half of the day is for us, and the festive meals are the half for us. Thus the eating on Erev Yom Kippur is the half which is for us, and on Yom Kippur we pray the entire day, and that is the half for Hashem. Rabeinu Yonah says another reason; it is a Mitzvah to eat on Erev Yom Kippur because we need to be happy that we have arrived at this day. The Sefat Emet says another reason why it's a Mitzvah to eat on Erev Yom Kippur; on Erev Yom Kippur it's a Mitzvah for each person to appease his fellowman. And it's only natural that when a person is fasting he is tense and his heart is not receptive to listening to his friend. Therefore the Torah said to eat in order for a person to have the heart to forgive his friend, as it is written regarding Boaz "And he ate...and his heart was satisfied". (Megillat Rut 3:7)
"For on this day shall atonement be made for you, to purify you; from all your sins shall you be purified before Hashem." (Vayikra 16:30)
Rabbi Yisrael Salanter says that if Yom Kippur was even only once in 70 years, we would need to be happy, all the more so that it comes every year.
"Al Chait...V'Al Chait" (in English: "For the sin....and for the sin...")
We say "Al Chait" according to the order of the Hebrew Alphabet, twice. One time we say "Al Chait", and another time we say "V'Al Chait". The reason the confession covers every letter of the Hebrew alphabet is in correspondence to the Torah which we have sinned against, since the Torah was written with every letter of the Hebrew Alphabet. And why do we cover the Hebrew alphabet twice? One time corresponds to sins between man and Hashem, and another time corresponds to sins between man and his fellow man.
"And they shall confess their sin which they have done..." (Bamidbar 5:7)
Vidui (In English: Confession) is a positive Mitzvah from the Torah, as it is stated in the Torah Portion of Naso: "And they shall confess their sin which they have done..." The main point of confession is to abandon the sin, and one strikes his heart to as if to say "you (my heart) have caused me to sin".
The Book of Yonah (Haftorah read in the afternoon service of Yom Kippur)
The Rav of Brisk ztz"l emphasizes that in the Haftorah of Yonah, that there were all kinds of people from the 70 nations of the world in the boat, and all kinds of idol worship, and the righteous person Yonah says "I am to blame" as it is said, "because of me there is this big storm". The reason for this is that a Tzaddik (righteous person) always places the blame upon himself.
"P'tach Lanu Sha'ar" (in English: "Open for us a gate", from the Ne'ila prayer)
It is written in the Holy Books, that just as every gate has a specific key to open it, but an axe can open every gate; so too in the Upper Realms every "Heichal" (in English: "Hall") can be opened by means of specific Kavanot (in English: elevated and/or Kabbalistic intentions during prayer), but a broken heart and submission to Hashem and crying are like an axe that can open all the Halls. It is written in the Zohar that there is a Heichal (Hall) and a treasure which is opened only one time in the year at the time of Ne'ila (the final prayer on Yom Kippur). This treasure has within it all the goodness in the world -- atonement, forgiveness, an emanation of abundance, and everything good. If so, we need to strengthen ourselves very much at the time of Ne'ila in order to receive this emanation of abundant blessings.