John was standing with two of his disciples, and as he watched Jesus walk by, he said, “Behold, the Lamb of God.” The two disciples heard what he said and followed Jesus. Jesus turned and saw them following him and said to them, “What are you looking for?” They said to him, “Rabbi” (which translated means Teacher), “where are you staying?” He said to them, “Come, and you will see.” So they went and saw where he was staying, and they stayed with him that day. It was about four in the afternoon. Andrew, the brother of Simon Peter, was one of the two who heard John and followed Jesus.
He first found his own brother Simon and told him, “We have found the Messiah,” which is translated Christ. Then he brought him to Jesus. Jesus looked at him and said, “You are Simon the son of John; you will be called Cephas,” which is translated Peter.
John was the friend of the Bridegroom; he sought not his own glory, but bore witness to the truth. And therefore he wished not his disciples to remain with him, to the hindrance of their duty to follow the Lord; but rather showed them whom they should follow, saying, "Behold the Lamb of God." For He alone and singly is the Lamb without spot, without sin; not because His spots are wiped off; but because He never had a spot. He alone is the Lamb of God, for by His blood alone can men be redeemed. This is the Lamb whom the wolves fear; even the slain Lamb, by whom the lion was slain.
There were disciples of John who not only did not follow Christ, but were even enviously disposed toward Him; but the better part heard, and followed; not from contempt of their former master, but by his persuasion; because he promised them that Christ would baptize with the Holy Ghost. And see with what modesty their zeal was accompanied. They did not straightway go and interrogate Jesus on great and necessary doctrines, nor in public, but sought private converse with Him; for we are told that "Jesus turned, and saw them following, and said to them, 'What seek you?'" Hence we learn, that when we once begin to form good resolutions, God gives us enough opportunities for improvement. Christ asks the question, not because He needed to be told, but in order to encourage familiarity and confidence, and show that He thought them worthy of His instructions.
Observe then, that it was upon those who followed Him, that our Lord turned His face and looked upon them. Unless you by your good works follow Him, you shall never be permitted to see His face, or enter into His dwelling.
Tract VII on the Gospel of John (St. Augustine)
Homily XVIII on the Gospel of John (St. John Chrysostom)
Explanations on the New Testament (St. Theophylact of Ochrid)