Isn't it a great concept?
But what's behind it? Is it the belief in immortality?
I guess every person who is looking at this concept is creating his own meaning.
You can believe in karma, and try to become a good person. And you can believe that there's no escape from this earth and this consciousness, and do whatever you like.
Maybe we all have a single soul, and while you are alive you give your personality to people around you and go on living in the generations to come. That's also immortality and reincarnation. Of sorts.
I don't think that immortality is quite the same as reincarnation. Wikipedia says that physical immortality is "a state of life that allows a person to avoid death and maintain conscious thought". Reincarnation requires you to die in order to be born again. I guess when you are reincarnated you still have conscious thought. You probably wouldn't say that conscious thought is "maintained" though, since it has to be interrupted. People don't usually actually remember what they were thinking about in their previous life, assuming they had a previous life.