What he means when he says this is that everyone has to leave something behind when they die if they want to be remembered. He is not saying that everyone does leave something behind. But he is saying that if you do not leave something behind then no one will remember you and your life will have been fairly pointless.
He says that the thing you leave behind can be just about anything. It just has to be something that you changed in some meaningful way. If you do leave something behind like that, he says, your soul has somewhere to go when you die.
As Ray Bradbury's science fiction classic Fahrenheit 451 nears its conclusion, Montag has found a new home, so to speak, with the groups of wandering exiles who have committed to remembering the literary works of the past -- the sources of knowledge and inspiration deemed threatening by the government they have all fled -- he engages in conversation with Granger, one of the unofficial leaders of this particular group. During that conversation, Montag laments his inability to remember anything substantial about his wife, Mildred:
"I can't remember anything. I think of her hands but I don't see them doing anything at all. They just hang there at her sides or they lie there on her lap or there's a cigarette in them, but that's all."
This uncomfortable admission by the former fireman sets the context for the comment by Granger:
"Everyone must leave something behind when he dies, my grandfather said. A child or a book or a painting or a house or a wall built or a pair of shoes made. Or a garden planted. Something your hand touched some way so your soul has somewhere to go when you die, and when people look at that tree or that flower you planted, you're there."
What Granger means by these comments is that the life lived well is the life that leaves behind something tangible and positive, such as some concrete indicators that the deceased had once lived, and that he or she left the world a better place than he or she found it. Mildred had lived an intellectually and emotionally empty existence, the perfect citizen of the dysfunctional authoritarian society from which Montag broke. She existed, but she never lived; she never created something to prove that she had once lived a meaningful life. Many people hope that, when they will have passed from this earth, that they will leave behind some measure of their significance as human beings, whether it is productive, well-raised children, trees planted in barren land, art that will adorn a wall somewhere, or any other tangible proof of a worthwhile life. Mildred left nothing behind to remind others that she had once existed. Montag regrets that, and Granger's words provide the emotional sustenance he needs to ensure that he does not repeat that mistake.
I agree with the above answer. Granger is saying that if you want to remembered and cherished after you're gone you must leave something behind you. Think of the people that leave charity organizations as their namesakes. Everyone that's remembered leaves behind some quote, story, drawing, song, play, organization, etc. But whatever you leave behind has to have some kind of proof of that persons personilty or life. A quote that a person is remembered for can tell you a lot about how that person lived.