What we miss with the English is that Peter is answering with a different word. Jesus is using "agape" while Peter is answering with "phileo".
"He said to him again a second time, 'Simon, son of Jonah, do you love (agape) Me?' He said to Him, 'Yes, Lord; You know that I love (phileo) You.'" (John 21:16)
This is a repentant Peter. He implied before Jesus' death that his devotion was so great for Jesus that it was greater than others were (Matthew 23:33, 35). In his first question, Jesus asked if Peter had agape greater than all the others. Peter could only answer that he had phileo for Christ. In this second question, Christ has dropped the "more than these," lessening the requirement. Peter still only answers he has phileo for Jesus. This humbles Peter who now recognizes his weakness. Now we can see why Peter was grieved with the third question.
"He said to him the third time, 'Simon, son of Jonah, do you love (phileo) Me?' Peter was grieved because He said to him the third time, 'Do you love (phileo) Me?' " (John 21:17)
Christ had dropped the requirement to only brotherly affection, which Peter had been saying all along.
What is the Bible definition?
What is this Greek word "agape" as the Bible defines it? In Mark 12 we find Jesus stating:
"'And you shall love the Lord your God with all your heart, with all your soul, with all your mind, and with all your strength.' This is the first commandment. And the second, like it, is this: 'You shall love your neighbor as yourself.' There is no other commandment greater than these.” (Mark 12:30-31)
Here the word Jesus used was "agape." In 1John 5:3 we find:
"For this is the love of God, that we keep His commandments. And His commandments are not burdensome."
What does James say about God's law?
"If you really fulfill the royal law according to the Scripture, 'You shall love your neighbor as yourself,' you do well; " (James 2:8)
The first four commandments of God's law tell us how we are to treat Him. God also is our neighbor in the universe (Jeremiah 12:14). He is the neighbor that rules. Therefore, we see that loving God and our fellow man - as translated from the Greek word Agape – manifests itself by keeping God's commandments. It is not just FEELING good but it is DOING good: “. . . love is the fulfillment of the law." (Romans 13:10).
A special relationship within the church
Besides keeping all God's commandments, the true church of God is to have a special family relationship. Here is where the Greek word STORGAY is within a compound word with PHILEO. The King James Bible states that Paul taught that those who believe in God should be:
"Be kindly affectionate to one another with brotherly love, in honor giving preference to one another; " (Romans 12:10)
The Greek word translated as "kindly affectionate" is philostorgos (Strong's Concordance #G5387) and means a loving friendship-family relationship. One day when Jesus taught the crowds, his mother Mary and his brothers came to visit him. When he was told his mother and brothers came to see him Jesus said:
"But He answered them, saying, 'Who is My mother, or My brothers? . . . For whoever does the will of God is My brother and My sister and mother.' " (Mark 3:33, 35).
Believers, just like Jesus, are to consider and treat those who obey God and do His will as if they were close family members! This is the definition of love in the word of God.