God loves the world.  Christians talk a lot about love. It's one of the very first ways that God revealed himself to man. God created man, and pursued a relationship with him. 

The world (and the people in it). This world is not the way it should be. We're selfish, self-centered, willing to hurt others for our own gain. And even though we've been taught the Golden Rule since kindergarten, it's just as hard now to treat others with respect and dignity as it was to share our toys back then. 

He gave his only Son. Jesus is the Son of God. Two thousand years ago, a baby boy was born to an unwed teen in the stable of an inn in a backwater town in a Roman occupied state. His first visitors were outcast shepherds, who had seen visions in the sky of angels singing. He was named Jesus, and eventually grew up to be an itinerant preacher, gained a small following, and taught about the kingdom of God, healed the sick, and fed the hungry. He even forgave people of their sins. He defied the authority of the religious leaders, who became so concerned about him that they plotted his death. He was captured, accused, and sentenced to death by crucifixion. He died after being beaten, scourged and hung to a pole by nails through his hands and feet. He was buried in a tomb, and three days later his followers came to embalm him, but found the tomb empty. Jesus appeared to them, in the flesh, and hundreds of other eyewitnesses. 

Whoever believes in him should not perish. Death is not an ending. CS Lewis says, "..But it is immortals whom we joke with, work with, marry, snub, and exploit— immortal horrors or everlasting splendours." We have souls that will go on after the physical body decays. And in eternity, we will either be with God, or not. The choices we make in this life, to reject or accept God, crystallize in the next life. 

We are all destined to eternity without God, because of sin. We have separated ourselves from a holy and perfect God by our sin and rebellion. But Jesus offered himself as a sacrifice, the one perfect sacrifice. He takes the punishment that was meant for us. So by saying we believe in him, we say we want Jesus to be our perfection and holiness and sinlessness, things we will never have by our own effort.

But have eternal life. God is the source of all life. To be with God is to have eternal life. And that isn't just something we get after we die, but something we can experience now, while we are still on this earth.