I hate to use a hollywood movie to illustrate my belief, but it was the movie about a dragon, whose voice was Sean Connery. The protagonist asked the dragon why did he not just give up and die since he was the last dragon. The dragon said that he would not kill himself because he feared losing his soul.
Gods word tells us that He created us in His image. That does not mean that our physical body with its metablism and electrical impulses are "in His image". Even the beast of the forest have those attributes. But rather it is another part of us that is "in His image". We call it the soul.... and it is the very essence of man and the "real" us. It is what we mean when we speak of looking beyond a person's appearance or deep within to see who a person really is. And it is the soul that will continue to live on after the body dies.
Granted that it is difficult for the finite mind to grasp the concept of a spirit or soul. And we must take Gods word for it on faith. But then, we cannot fully grasp the existance of Physicist's (another freeper) "linear collider" either, can we? But we take it on faith that he and other scientists understand that which we cannot fully grasp.
We see glimpses of the essence of the soul if we look. Next time you are talking to someone, look deep within their eyes, listen to the "tone" of their voice.
There is more.... but I hesitate to go there. The scriptures say that there will come a day when God will resurrect those dead bodies, repair them, and reunite them with thier souls. Even harder to grasp. If you are courious its all there in God's word.