1. On Rosh Hashanah, judgement of the world commences and the concept of justice reigns.
On Yom Kippur, judgement of the world is concluded and the concept of mercy and forgiveness reigns.
2. The central concept of Yom Kippur is that of Teshuvah (repentance).
They asked G-d, 'what is the punishment of the sinner?' and he replied, 'let him repent and I will accept him - as is written in the Psalms (25:8),
"G-d is good and upright".'
3. Moses ascended Mount Sinai three times:
(a) From the 7th of Sivan to the 17th of Tammuz - in order to receive the first two tablets of the Torah;
(b) From the 18th of Tammuz to the 29th of Av - in order to pray for Israel (after the sin of the Golden Calf);
(c) From the 1st of Ellul to the 10th of Tishrei (Yom Kippur), when G-d was reconciled with Israel.
4. The Vidui is said ten times on Yom Kippur:
- twice in Ma'ariv;
- twice in Shacharit;
- twice in Mussaf;
- twice in Minchah;
- once in Ne'ilah;
- and once in Minchah on Erev Yom Kippur.
Confession is the fundamental basis of repentance.
5. Blowing the Shofar at the end of the concluding service (Ne'ilah) is a reminder of the blowing of the Shofar on Yom Kippur itself at the Yovel (Jubilee Year) (Leviticus 25:9-10).
6. After the havdalah at the end of the fast, it is customary to hammer in the first nail of the succah in accordance with the concept of, 'one Mitzvah leads to another' and the verse,
'they go from strength to strength.' (Psalm 84:8)