This quotation is from Edmund Burke's Reflections on the Revolution in France. Burke took a disapproving attitude to the Revolution, which was not necessarily what would have been expected of him—he had advocated for many other liberal causes, including the American Revolution and the disentanglement of his home country, Ireland, from British rule. However, Burke felt that the French revolutionaries were not conducting themselves in a way which was productive, or which would help them form the kind of society which he felt should be striven towards at all times.
Burke disapproved of the French Revolution because, unlike other revolutions, he felt that it was an attack on what was fundamental to French civilization itself, rather than an attempt by a disenfranchised people to free themselves. He noted that part of what makes society function is for us to be defined by the "subdivision" of it to which we belong. The Revolutionaries wanted to destroy subdivisions of this sort, and make society uniform. A society of that sort, Burke suggests in this quotation, is not a society at all.
Burke describes society as a contract, not only between the people currently trying to survive together in a country which needs to be economically successful and provide for its inhabitants, but also between these people and the people who birthed that society, as well as the people who will come to inherit it. Therefore, the people who are currently inhabiting French society cannot behave simply in order to further their own goals—emancipation from the Church and the nobility—without thinking of how this will affect those who will follow them, or how disrespectful it might be to those who have helped form this society. Rather than focusing on lofty ideals like making all men equal, the Revolutionaries should be thinking about how to preserve their country in the best and most economically sound state for future generations.
Burke felt that the French Revolution failed to acknowledge that the best of French civilization, specifically its learning and manners, came from the nobility and the clergy. He is suggesting, therefore, that to destroy the nobility and the clergy would be to destroy the society's capacity to sustain itself. This would be terrible for future generations, in his mind, and would therefore break the contract that should exist between a people and their ancestors and descendants.
This idea of Burke's is, of course, widely applicable beyond the French Revolution. It can be applied to modern day concerns such as global warming, with the idea being that we all have a duty to protect our world, not for ourselves only, but for those who will follow us. But Burke's particular concerns are with the material success and wealth of France, how these will be affected by revolution based on what he considered flimsy principles, and how this might betray future generations.