Imagine a young girl asleep on the second story of her home. She awakes one night—middle of the night—and there is the smell of acrid smoke. She stumbles to the door and opens it to a sheet of fire. The young lady slams the door against the flames and stumbles to the window and stares down into the smoke and the darkness. From the ground below the young lady hears her father's voice saying, "Honey, jump!"
The young lady replies, "But, Daddy, I can't see you."
The father replies, "It's all right, Honey, I can see you. Jump!"
So the young lady jumps into her father's arms.
Now it's a part of faith for that young lady to believe her father is there. It's another part of faith to believe in her father, to feel that her father is able to catch her. It's the essence of faith to throw herself into a father's waiting arms.
That's what it means to believe on Jesus Christ. It's a part of faith to believe Jesus died on the cross to take the punishment for your sin; it's another part of faith to believe God is able and willing to forgive you and give you eternal life. It's the essence of faith to abandon yourself to God completely and allow Jesus Christ to be your Savior.
John Wesley, founder of the Methodist movement, expressed it well when he said that to believe on Jesus is "casting yourself with a reckless abandon on the grace of God."
Belief that brings us to God is as simple and life-changing as that. (Haddon Robinson, "True Believers")