Rosh Hashanah and Yom Kippur are the High Holy Days of the Biblical calendar.
While Rosh Hashanah is a joyous time, Yom Kippur is very serious. It is the Day of Atonement, when we seek forgiveness of our sins.
"The L-RD said to Moses, 'The tenth day of this seventh month is the Day of Atonement. Hold a sacred assembly and deny yourselves, and present an offering made to the L-RD by fire. Do no work on that day, because it is the Day of Atonement, when atonement is made for you before the L-RD your G-d...You shall do no work at all. This is to be a lasting ordinance for the generations to come, wherever you live. It is a sabbath of rest for you, and you must deny yourselves. From the evening of the ninth day of the month until the following evening you are to observe your sabbath."
(Leviticus 23:26-28, 31-32, NIV)
The Bible teaches that sin separates us from G-d.
"Surely the arm of the L-RD is not too short to save, nor His ear too dull to hear. But your iniquities have separated you from your G-d; your sins have hidden His face from you, so that He will not hear." (Isaiah 59:1-2, NIV)
During the Day of Atonement in ancient days, the High Priest offered the blood of a sacrificed animal to make an atonement, or covering, for sins.
"For the life of a creature is in the blood, and I have given it to you to make atonement for yourselves on the altar; it is the blood that makes atonement for one's life." (Leviticus 17:11, NIV)
These days, Jews fast and pray, repent, and ask G-d's forgiveness on Yom Kippur. Since there is no longer a Temple or High Priest in Jerusalem, they cannot offer the required sacrifice. Rabbis teach and hope that good works and prayers will be enough to cover sins.
Messianics believe that G-d's requirement of a blood sacrifice has not changed. They teach that the requirement has been fulfilled, however, in the atoning blood sacrifice of Jesus, as recorded in the New Testament.
"But now a righteousness from G-d, apart from law, has been made known, to which the Law and the Prophets testify. This righteousness from G-d comes through faith in Jesus Christ* to all who believe. There is no difference, for all have sinned and fall short of the glory of G-d, and are justified freely by His grace through the redemption that came by Christ Jesus. G-d presented Him as a sacrifice of atonement, through faith in His blood." (Romans 3:21-25, NIV)
Whether Messianic or not, prayer, fasting and rest are powerful ways to get closer to G-d. I encourage you to pray this prayer of David during your Yom Kippur observance:
"Open Thou mine eyes that I may behold wondrous things out of Thy law."
(Psalm 119:18,JPS)
You might want to plan a special meal for after the fast.
*The word Christ is the Engish version of the Greek word Kristos. It is the same as the Hebrew word Meshiach: It means Messiah.