I don't get it. Why does thinking ACTUALLY work? And how?

The more I talked to Claude about this subject, the more confusing it got for me. It told me that spending more time reasoning about a problem makes Claude provide better results, but that it's not necessarily a creative process. Then why is thinking useful? What does it actually provide to Claude? More context? Isn't that context already what I would normally get? In what direction does it change the conversation? And why "better"?? Why not "slightly better" or "slightly worse"? How is that measured, and how do I know it ACTUALLY helps? Is that quantifiable? Or is it like fiat - we have a consensus that it has value, so it has value?