What Is The Meaning Behind The Song, Jesus Loves Me This I Know?

The meaning?...I've never studied who wrote it and what their purpose was, but I know the message it allows the singer to proclaim.

"Jesus loves me, this I know." No doubts.
How? "The Bible tells me so."
"Little ones to Him belong." This is twofold: As a young child, it notes that even they can grasp God's gift of salvation, and be a follower of God. As an adult, even we are small in comparison to God, and we need to remember that.
"We are weak, but He is strong." God is Sovereign, not us...even if we think we are.
Yes, Jesus loves me! Proclamation
The Bible tells me so. Proof of what followers of Christ believe.

To assert His love for you, to commemorate His body being broken for mankind, and to express the joy of experiencing freedom and peace in God. It's something you can't get just going to church or reading the Bible, or saying you believe in God.