To expand on what Spunky said, it’s a 25-hour period of fasting for those who are able to do so, reflection, and remembrance.
It’s also called the Day of Atonement or Day of Judgement.
Services revolve around prayers of personal repentance and memory of departed loved ones.
It is said that God writes our names in the Book of Life on Rosh Hashanah, which is the first two of 10 days of awe, and seals the book on Yom Kippur, which is the 10th day.