How did the church save civilization, as some historians have suggested, in the western world?

One could debate exactly what is included in
"civilization" or the "western world." Because your tags include reference to "history
of the catholic church in western civilization," the response becomes easier to
define.

The Roman Catholic church became the preserver of
much of the structure upon which western civilization was built during the so-called
Middle Ages - the period of time ranging roughly from the fall of Rome and the Roman
Empire in 476 CE to the Renaissance in the 1400s.

The
Church hierarchy of priests, bishops and other leaders served as advisors to the feudal
lords and kings who exercised whatever political control there was in a given area. Any
education that was delivered during that time came through the Church, as children were
trained to assume roles of responsibility within religious organizational systems. Some
monastic orders preserved the history and traditions of previous civilizations as a part
of their mission to create the manuscripts that recorded the historic writings saved
from destruction.