Hello!
To know the melting or boiling points of substances is extremely important:
-In a Scientific Setting, it would help identify and separate unknown substances, as the melting or boiling points are unique for each compound, and their determination is useful for identifying and separating them.
-In an Industrial Setting, it would help engineers to know the storage temperatures of compounds. Some compounds if stored at temperatures above their boiling points will evaporate and when stored at temperatures under their melting points will solidify. In some cases this behavior is undesired and knowledge of boiling and melting points is important.
Have a nice day!