In addition to other answers discussing the examples we make for generations that look up to us, there’s the more obvious “environmental” inheritance. If we continue to pollute the Earth and kill of species, then our children will inherit a the ruined product of our inactions; imagine kids being born and never having known or seen polar bears? Or thinking that it’s completely natural for the ocean to be full of plastic— because they’ve never known anything else? The earth is something we all share, and even after we are gone, future generations will still have to live there. I like comparing it to a house of sorts. This is the only house we have, passed down from parent to child. If the parent ruins the house, gets it all dirty, breaks things, lets it go to rot, etc. then even if they won’t be around to see the effects, their children will be left to deal with their mess. So then we are responsible for keeping our house clean for future generations (with the house representing the Earth obviously).
In addition we carry down systems too. If we create a horrible, restrictive government, then our children will be born into a world knowing nothing but restriction. It is our job to take care of what we have and make sure future generations are given the same, if not even more than we were.