Yom Kippur, the Day of Atonement, falls on the 10th of Tishri — five days before the Feast of Tabernacles (Sukk'ot). It is a very solemn fast day, a special Sabbath, but NOT one of God's three ordained High Holy Days.
Regardless of what secular media announces, God has NOT declared Yom Kippur a High Holy Day. Modern "cultural" Hebrew religious authorities attribute far more importance to Yom Kippur than is Scripturally warranted or defensible.
Yom Kippur is, however, a serious day of fasting, prayer, and repentance in the Hebrew tradition — and its themes of atonement have profound Messianic significance pointing to Christ Jesus as the ultimate fulfillment of the Levitical sacrificial system.