Explain the following quote: "All the good things which are connected with manners and with civilization, have, in this European world of ours, depended for ages upon two principles: . . . the nobility and the clergy" (193).

The quote you have shared is from the politician Edmund Burke's pamphlet Reflections on the Revolution in France, which was published in November 1790. The French Revolution had begun in 1789 with the formation of the National Assembly, which challenged the structure of French society. The Revolution quickly gained momentum and the authority of the aristocracy and the clergy —formerly France's ruling classes—rapidly dissolved. The National Assembly took control of the government and began abolishing the laws which had propped up the nobility and the clergy for generations. France was in a state of turmoil, interspersed with bouts of serious violence. France was a major world power at the time, so its abrupt descent into chaos was shocking to many nations.
Edmund Burke is writing from that shocked point of view. He is horrified to see this once-great nation falling apart, and he believes that the actions of the revolutionaries will only cause more problems in the long run. They may want liberty, equality, and fraternity, but by destroying their ruling classes and tearing down their old institutions, the revolutionaries are only hurting themselves.
This is the point of the quote you are asking about. Burke says:

Nothing is more certain than that our manners, our civilization, and all the good things which are connected with manners and with civilization, have in this European world of ours depended for ages upon two principles, and were indeed the result of both combined: I mean the spirit of a gentleman and the spirit of religion[, that is, the] nobility and the clergy.

Everything that was good about France, which made it wealthy and powerful, was the result of the social structure which the revolutionaries are tearing down. Society needs ruling classes, Burke argues, to "keep learning in existence even in the midst of arms and confusions." The aristocracy and the clergy are the protectors and promoters of all the better things in life—art, music, literature, education, and spirituality. Without an aristocracy or a clergy, French society will "decay." Burke predicts a terrible future for the French if they do not stop this revolution in its tracks and restore society to its former status:

[I]f commerce and the arts should be lost in an experiment to try how well a State may stand without these old fundamental principles, what sort of a thing must be a nation of gross, stupid, ferocious, and at the same time poor and sordid barbarians,—destitute of religion, honor, or manly pride, possessing nothing at present and hoping for nothing hereafter?