This Scripture calls to mind the death of Jesus on the cross, and so it should. We should also remember what immediately preceded these words in the Lord's final address to his disciples: "This is my commandment, that ye love one another, as I have loved you." Jesus was not only speaking of his own sacrificial death; He was reminding us that we must also lay down our own lives for one another.
Practically speaking, what does it mean to lay down your life for others? Jesus answered this question by example, with the love He showed for his disciples. At every turn, He was intent on caring for those the Father had given Him - physically (Mark 6:31), emotionally (John 14:1), and spiritually (John 16:33). He encouraged, and He rebuked; He washed their feet, and He upbraided them for their unbelief. In everything, He concerned Himself only with what was good for them - not with gratifying Himself or enhancing his own popularity.
Everything Jesus did for his friends was love, because it all flowed from a perfect heart with right motives. We have no perfect lives of our own to lay down for each other, but through power of the Holy Spirit we can participate in the same righteous Life that set the example for us. Our natural selfishness can be replaced by a supernatural love that causes us to lay down our lives for the eternal benefit of others.
All Scripture references from KJV. Commentary ©2012 Hitchcock Family Ministry. Unaltered text may be reproduced freely without financial gain. Original commentary and Scripture song available at http://www.freescripturesongs.org/greater-love-hath-no-man-than-this.