Trees occur in various venues in computer science: decision trees in algorithms

Trees occur in various venues in computer science: decision trees in algorithms search trees and so on. In linguistics one encounters trees as well typically as parse trees which are essentially sentence diagrams such as those you might have had to do in primary school breaking a natural-language sentence into its componentsclauses subclauses nouns verbs adverbs adjectives prepositions and so on. What might be the significance of the depth and breadth of a parse tree relative to the sentence it represents? If you need to look up parse tree and natural language processing on the Internet to see some examples.