This year Yom Kippur begins at sunset on September 26, meaning, the 27th is a High Holy Day on which we fast and take the day off from work.
Yom Kippur is a Shabbat/High Holy Day on which we fast, repent and bare our souls to YHWH, asking Him to forgive us anything we may have done throughout the year that was not pleasing to Him: This solemn day represents the need for the sacrifice/sin offering that must be made for the sins of the nation.
Yeshua, of course, WAS that "Sacrifice" (actually, "Offering" is a better word, because no one "sacrificed" him; he martyred himself), and he will be recognized for it at the Marriage Supper of the Lamb which may (judging by how close together the Fall Festivals are) take place immediately after Rosh Hashana/the "catching-up of YHWH's people" just BEFORE we all return with Him to fulfill the Feast of Tabernacles, wherein Yeshua will "tabernacle" among us for the next thousand years!
Celebrated on Tishri 10, this mo'ed falls in the September/October time frame. Leviticus 16:29 tells us: "It is to be a permanent regulation for you that on the tenth day of the seventh month you are to deny yourselves and not to do any kind of work, both the citizen and the foreigner living with you. For on this day, atonement will be made for you to purify you; you will be clean before ADONAI from all your sins. It is a Shabbat of complete rest for you, and you are to deny yourselves. This is a permanent regulation."
This Festival represents the need for the sacrifice/sin offering that must be made for the sins of the nation. As the Bible tells us, Messiah shall descend to put to an end the sins of Israel. (Remember, "Israel" includes ALL who believe in and follow the God of Abraham, Isaac and Jacob!)
At that time the Jews will mourn for the "One who was pierced" and FINALLY recognize that Yeshua was the Messiah, all along! This day will be fulfilled upon the Second Coming of Messiah to the Earth (Matt. 23:37-39, Hos. 5:15 thru 6:1-3, Zech. 13:8,9 Zech. 12:10, Zech. 13:1, Ezek. 16:61-63).
This holy day signals the call for repentance, for the time is short and Judgment is coming upon the Earth - whether people are ready, or not! (See the Books of Daniel and Revelation.)