Curiosity is important in the progress of science because it

Curiosity can be illustrated as the emotion or behavior of being curious, considering a feeling to attain information or knowledge. Curiosity as emotion and behavior is considered as the mediating force not only for the growth and development of human beings, however, also for the progression and advancements in language, science, and industry.  

It is an essential part of the development of science as it is the curiosity that develops the tendency in someone to invent or discover something. It is their tendency of questioning that helps them to look for the answers, that is, it is their curiosity, which helps them to find a solution to an issue.