Bread is the cross, and fish are 'every word that proceeds from the mouth of God'.
Using the motif of Three things (hearing, seeing, walking) :
After the resurrection, Peter had heard Jesus teach, and he had seen the scars, but in this third visit with Christ he was not yet walking with him... he was still not reconciled after his thrice denial.
Peter has 'returned to his vomit' (2Pe 2:22 )... his old life as a fisherman even though he knew Jesus was resurrected. We find him doing everything wrong: he is naked, in the dark, and fishing from the left side (goats are on the left). Also he has led other disciples to do the same with him.
Jesus said that "man does not live by bread alone, but by every word which proceeds from the mouth of God." (Mt 4:4) He also said that the bread was his body which was given for us. (Lu 22:19 ) So, we can say that man does not live by the cross alone, but by every word which proceeds from the mouth of God.
But he always served fish with the bread, so fish represent "every word.”
Jesus asked Peter if he had any meat. The meat offering was actually bread (Le 2:1 ) which was offered as a fellowship offering. Peter had no fellowship to offer.
Jesus had provided bread and fish for them. He was reconciling them, and particularly Peter, to himself.
Jesus then commands Peter to "feed my sheep.” Well, what is he supposed to feed them? 153 fish. Every word which proceeds from the mouth of God. Jesus provided fish for Peter, and Peter alone, at Jesus's command, pulled the 153 fish from the water, when the other fishermen together couldn't bring in the catch.
The lesson for Peter is that not only was he reconciled to Christ, but by obedience to Christ he would have the word of God in sufficient supply to feed the sheep of Christ. 153 = 144 + 9. 144 for the church and Israel. The nine left over are for the three who each are the fullness of God.
The story ends with Peter walking with Jesus. We hear, see and walk in response to his word, works and life.
When we are walking by every word, we have communion with all three persons of the Godhead, who are each fully God.