* The intensity of something:
* "All students benefited from the program to a greater or lesser degree." (Some students benefited more than others.)
* The prevalence of something:
* "The new policy affected different departments to a greater or lesser degree." (Some departments were more affected than others.)
* The extent of agreement or disagreement:
* "Everyone agreed with the proposal, to a greater or lesser degree." (Some people were more enthusiastic about the proposal than others.)
Essentially, it acknowledges that there are variations in the way something applies or manifests itself, avoiding absolutes.