At the last supper, while Jesus and His disciples were eating, Jesus began to speak about the betrayal and the death He was about to experience. As a farewell sermon to his disciples, Jesus spoke about many things, one of which is love. He said,
Greater love hath no man than this, that a man lay down his life for his friends (John 15:13).
Hours after saying this, Jesus and His disciples were in the garden of Gethsemane. There, Jesus prayed fervently and He was strengthened from on high to face what was yet to come. Soon after He was done praying, a band of people, composed of soldiers and some officers, sent by the Jewish religious leaders came there. One of them was Jesus’ disciple who went by the name Judas Iscariot. He came to kiss Jesus and immediately Jesus was arrested. They sent Him straight to the palace of the high priest to stand trials.
There, they managed to find Him guilty of blasphemy and, in the early hours of the morning, He was sent to Pilate the governor. In the governor’s presence, they accused Him of subverting the people and claiming to be the king of the Jews. All along Jesus had been silent to His defense.
After long proceedings, by popular request, Jesus was condemned to crucifixion. Before facing the cross, He was mercilessly beaten by the Roman soldiers and then was made to carry His cross. Eventually, He was taken to Golgotha. And there, He was nailed to the cross and the cross was erected for all people to see Him hanging. He was mocked by soldiers, the Jews, and the Jewish leaders.
The truth is, Jesus did not die because His enemies were able to overcome Him. His death was a sacrifice. He willingly allowed His enemies to arrest Him, try Him, beat Him, and kill Him because He was doing it to save us. If Jesus laid down His life for us, then according to John 15:13, that is how He showed His greater love.
So when Jesus said, “Greater love hath no man than this, that a man lay down his life for his friends”, He was indirectly talking about His own sacrificial death which would be a display of His greater love for mankind.
Relevant video on how Jesus showed His greater love to man.
This is how Jesus showed His greater love for us – by suffering and dying to save us from sin, Satan, death, and the wrath of God.