Curiosity is important in the progress of science because it....?

The scientific method:
1. Observe something.
2. Formulate a hypothesis.
3. Devise a test.
4. If the test fails, go to #2.
5. If the test passes and is confirmed, the hypothesis might be promoted to a theory and used to prove other hypotheses. And it might not.

Without curiosity, step #2 never happens.