HaShem said to Moshe that the tenth day of the month of Tishrei would always be Yom Kippur, the day of forgiveness, and He commanded Moshe to teach the Jews to observe Yom Kippur forever! But after the Beit HaMikdash was destroyed, there was no longer a Kohein Gadol, or a Kodesh Hakedashim. How would the Jews keep Yom Kippur?
Since korbanot (sacrifices) could no longer be offered, HaShem gave new laws to replace the service that the Kohein Gadol once did. The korbanot were very precious to HaShem - but the Jews themselves are far more precious. So, the korbanot were replaced with the service of prayer. On Yom Kippur, we pray all day long, asking HaShem for forgiveness. And every Jew who is over the age of Bar or Bat Mitzvah fasts - they don't eat or drink anything for the entire night and day.
More than any other day of the year, our prayers on Yom Kippur have special power. The day itself is filled with the powerful energy of HaShem's forgiveness.
If you have done anything that has hurt or wronged someone in any way during the past year, it's not enough to ask HaShem to forgive you - even if you spend all day praying! Before Yom Kippur, it's important to ask forgiveness of the people you have hurt. Then you can do teshuva and resolve to change for the better in the coming year. Once your friend forgives you for something you have done wrong, you can be sure that HaShem will forgive you, too!