God demonstrated his love for us by giving Jesus to die for our sins. Love is not just something that God demonstrates. God is love. Pure love is the very essence of who God is.
Walking alone the Mediterranean Sea one day, Saint Augustine was pondering the doctrine of the Trinity. He asked God to make him understand fully how He could be One, and yet be three. He seemed to hear a voice saying, "Pick up one of the large sea shells there by the shore." Augustine picked it up and heard the voice said, "Now pour the ocean into the shell."
Augustine replied, "Lord, I can’t do that."
The voice answered, "Of course not. In the same way, how can your small, finite mind ever hold and understand the mystery of the eternal, infinite, Triune God?"
Theology is the study of God. It is the most difficult field of study a man can pursue. It is impossible for the human mind to completely comprehend God. God wants us to know Him, but He also knows our limitations. He, for that reason, created in us a medium for knowing and being in fellowship Him. That medium is the medium of love.
No one really understands love. It is far more than just an emotion created by the interaction of chemicals and neurons in the brain. The good news is that we don’t have to understand love to experience it. We don’t have to understand God to know Him either. All we must do is experience His love
The Vietnam War was at its height during the spring and early summer of 1968. Richard Nixon was running for President of the United States. One of his campaign advisors was bothered by a Nixon ad which showed a photo of an American soldier in Vietnam with the word "Love" written on his helmet. He thought it made people think the hippie was saying, “Make love, not war.” He thought the soldier was making an antiwar statement. It tuned out that “Love” was the soldier's last name. He just wanted people to know who he was.
That’s how God tells us who He is. God is love.