After rebuking the Corinthians on the senselessness of their glorying in the face of such a scandalous incidents, the apostle went on to advocate cleansing of the Church by ‘purging out the old leaven’ (1Cor. 5:7).
The word ‘leaven’ is used in Scriptures to mean false doctrines and sin (e.g. Matt. 16:6-12; 1Cor. 5:8). It is also used literally to mean yeast that causes bread dough to rise prior to baking (eg. Matt. 13:33).
Here, it is used to symbolize sin, hence commanding them “to remove the old leaven (or nature) of sin, so as to be a really new lump (or clean body) (1Cor. 5:7). This point must be noted by any group of people who claim to be children of God.
Besides, the apostle had also argued that a little leaven leavened the whole lump. This is so literally, for it is a small quantity of yeast that causes the rising of the entire bread dough. In the same way, if sins, no matter how little are not expelled from a congregation, such a congregation will soon be full of sinners (cons. 1Cor. 5:6,)