Isaiah is in this vision in the temple, and is afraid that he, as a sinner, has entered the presence of God. In Isaiah 52:11 the Lord commands that the children of Israel “touch no unclean thing … be ye clean, that bear the vessels of the Lord.” The vessels referenced are temple vessels. Thus, Isaiah is declaring that he is in a position that should not be.
The solution is that one of the seraphim brings a coal from the altar and lays it upon Isaiah’s mouth. There are two images here. The first is that there is a burnt sacrifice on the altar. Burnt sacrifices atone for sin. Therefore, the seraphim declares: “this has touched thy lips; and the iniquity is taken away, and thy sin purged.” Isaiah has been offered as though he were a sacrifice, and cleansed through a symbolic burnt sacrifice.
The second image is that the coal is placed on his lips. This symbolically cleanses his speech, and perhaps declares that his words truly represent Jehovah’s.