Songfacts®:

• Clapton is saying that we live on through our children, generation after generation. He "knew" his father (finally) when he looked in the eyes of his son, Conor, and realized they were his father's eyes.
• Clapton was raised by his grandparents, who he thought were his parents until he was in his teens. Growing up, he never knew his father, who only contacted him after Eric was famous. The sadness at not having a relationship is evident in this song. >>>

  Suggestion credit:
  Steve - Long Island, NC, for above 2
• Conor Clapton died in 1991 at age 4 when he fell out of the window of a 53-story building in New York City in a freak accident (Eric wasn't there, but was planning to see him that day). Over the next few years, Clapton found solace on the island of Antigua, which is where he wrote the song, which appeared seven years after Conor's death on the Pilgrim album.
  
  "I wrote a song linking the loss of Conor with the mystery surrounding the life of my father, called 'My Father's Eyes,'" he wrote in Clapton: The Autobiography. "In it, I tried to describe the parallel between looking into the eyes of my son and seeing the eyes of the father I had never met, through the chain of our blood."
• In the lyric, "Just a toe rag on the run," "toe rag" is a slang term for a small child, street child, perhaps, in England.