Yom Kippur happens on 10 Tishrei each year and completes the 'days of awe' which began with Rosh Hashanah. The traditional belief is that this is the day when the Book of Life, which G-d opened on Rosh Hashanah, is sealed for another year. It is therefore an incredibly solemn day, with fasting and a prohibition on food, drink, leather shoes and sex.
Yom Kippur is also known as the "Day of Atonement" and is a time for reflection and repentance, as well as forgiving others. It is the opportunity for a fresh start in your relationship with G-d and with your fellow people. One way of honouring Yom Kippur involves giving tzedakah (charity).
For Israel, this year marks the 50th anniversary of the Yom Kippur War. If you want to know more about the background to it, you could do worse than read "Deceit of an Ally" by our friend Bruce Brill. It tells the stunning story that the United States government knew that Arab armies were planning to attack Israel in order to "drive the Jews into the sea", yet wilfully deceived its counterpart and supposed ally.