“Therefore that disciple whom Jesus loved saith unto Peter, It is the Lord. Now when Simon Peter heard that it was the Lord, he girt his fisher’s coat unto him, (for he was naked,) and did cast himself into the sea.”
That disciple whom Jesus loved said to Peter, 'It is the Lord!' When Simon Peter heard that it was the Lord, he put on some clothes, for he was naked, and jumped into the sea — the beloved disciple's perception (theological intuition) recognizes Jesus before Peter does, maintaining the beloved disciple's spiritual superiority. Peter's hastiness (putting on clothes and jumping in) contrasts with the beloved disciple's contemplative discernment. The sea separates shore (Jesus' location, eschatological reality) from boat (the disciples' current state), and Peter bridges this gap through impulsive faith-movement.
Church Fathers on John 21:7
The preceding words of the Evangelist seem to indicate the end of the book, but He goes on farther to give an account of our Lord’s appearance by the sea of Tiberias: After these things Jesus showed Himself again to the disciples at the sea of Tiberias.
He says, Afterwards, because He did not go continually with His disciples as before; and, manifested Himself, because His body being incorruptible, it was a condescension to allow Himself to be seen. He mentions the place, to show that our Lord had taken away a good deal of their fear, and that they no longer kept within doors, though they had gone to Galilee to avoid the persecution of the Jews.
The Evangelist, after his wont, first states the thing itself, and then says how it took place: And on this wise showed He Himself.