1 Corinthians 5:6 - Your boasting is not good. Don’t you know that a little yeast works through the whole batch of dough? Get rid of the old yeast that you may be a batch without yeast - as you really are. For Christ, our Passover lamb, has been sacrificed.
In Jewish culture the Passover meal was prepared without yeast. So the bread and everything else that would normally have it would be prepared without it. During this time the yeast represented sin, and removing it signified removing sin from your life.
Now, as Paul is talking in this passage he is comparing the church to a batch of dough. He reminds us that our Passover lamb, Jesus, has already been crucified and it is time to get the “yeast” out of the church. He is not talking about the people of the world (vs. 10), but those who know better.
Paul wants us to be careful of the people that call themselves Christians, but are still living a life of sin. They are willingly doing evil and trying to bring others down as well. Paul said not to associate with these kind of people. In fact, he goes as far as saying to get rid of them. They already know better and should be trying to live right, but refuse to.
Since these people will not change they are poisoning the whole body of Christ. Just as a little yeast works through the whole batch of dough, so these people will bring sin into the whole body of Christ. See, Christ, in His sacrifice, has already cleansed us of all our sin. Now it is our responsibility to keep the sin out. Love people but be careful of those who say they are Christians, but act like the world.