Peter had seen Jesus Christ. His readers had not. And although some of them were probably alive during the life of Christ, their location was distant, and they never had a chance to see him for themselves. Peter stresses that fact in this week’s passage.
You can see it for yourself in 1 Peter 1:8-9.
Peter had walked with Jesus, watching him perform miracles, hearing him teach, experiencing life with his Master. Since he had visually seen the Savior, it may have been easier for him to place his faith in him. But his readers, scattered around the world, had no such opportunities to see Christ. Peter makes a significant point out of this to reassure them in their struggles and suffering.
Peter had experienced the love of Christ first hand. Remember just before the crucifixion, Peter boldly stated that Jesus was the Messiah, and then rejected and denied him three times. At the end of John’s gospel, Jesus restores Peter by asking him three times if Peter loved him. Of course he did.
This experience probably set the stage for a certain level of amazement at the faith of his readers. He had see Jesus. He had had this conversation with Jesus about love. But the people to whom he is writing had not, and yet they still loved Jesus. I wonder if Peter was stunned at their level of faith, amazed that they could love without seeing.