Isaiah has made clear in the first 5 chapters that Judah has a big problem. How can Jerusalem, so full of corruption and idolatry, be transformed into something that resembles her destiny (Isaiah 2:1-4)?
One of the things chapter 6 shows us in answer to this is the pattern of covenant renewal. Isaiah not only comes as a sinner himself but on behalf of the nation. He is summoned into a vision (vv1-4), confesses his sin (v5), receives a gracious cleansing, completely apart from any of his own works (vv6-7), and then is commissioned to go (vv8-13).
There may also be a piece of the coal touching his lips that may be related to the consecration, his whole body offered up to the Lord in the smoke of that cleansing-coal.