There is a LOT of cultural context going on in this verse, but perhaps a good gist might be this: when at worship, the point is not ourselves, but Christ. This includes not putting the emphasis on ourselves in dress and in the Lord's Supper. Paul remembers the liturgy of that meal, a sacrament left to us by Christ himself, to remember his sacrifice and our connection to God. We are also connected to one another when we share that communion, but the focus is still Christ.