Future generations (persons who are not present today, not even born or conceived) are going to be affected, positively and negatively, by what present generations do.
Effects on future generations are often ignored when decisions about large-scale resource policies and about far-reaching technologies are made. Future discount rates used in economic planning effectively forbid planners from taking much notice of costs and benefits to be felt no more than thirty or fifty years in the future. This is now an anachronism, because it has become quite evident that technologies and environmental activities have reached a point where they have much more far-reaching effects on the future than before.
Whatever is right for our grand-children is always uneconomic and almost always impolitical.
Why do we care about the future? Our progeny. What are we trying to "sustain"? A healthy habitat 'primarily for them'. If we sought a sustainable habitat for various chemical eating microbes, diverse organisms and plants that thrive on our waste/pollution, we would happily continue our current behaviour. Shrinking biodiversity and killing off many species in our food chain will improve the sustainability for the remaining life forms better adapted to the altered environment.