The Eucharist is the high point of the Mass.  We recall how unworthy we are to receive the Blessed Sacrament, and ask God to forgive us of our shortcoming and fill us with His grace.  We ask for the prayers of our brothers and sisters in Christ, and they ask the same of us.  Paul is trying to tell the Corinthians that we are in this race together, and is beneficial and necessary that we help each other as a family.