Yom Kippur is the Jewish day of atonement.  It is a time during which Jewish believers seek forgiveness from God and their fellow men for wrongs they may have done in the previous year.

Jewish people are instructed in their Law to sacrifice as payment for their sins.  However, these days prayer has replaced the practice of animal sacrifices.

Yom Kippur is a special day, where the entire focus is prayer-- prayers of repentance and atonement.

 No, they don't!!

However, when Christians take communion, or the Lord's Supper as it is often called, the emphasis is also on repentance and atonement.  Like Jews, Christians also frequently seek forgiveness from God and from other people for wrongs they have done.  Communion is just a time for empasizing this and taking a specific time to get right with God and other people.

Jesus commanded that his followers do this to remember Him.  This purpose is not contrary to the idea of atonement.  In fact, it is what Jesus is all about.  Jesus is love, therefore this idea of declaring your love to God and others is perfect obedience to the command.

*Disclaimer: I am not an expert on Judaism.  I only understand the basic idea of Yom Kippur, and have drawn a parallel based on that.*