How much does your credit score matter for getting approved for a mortgage?

I’m starting to look into buying my first home and trying to understand how big of a role credit score actually plays. From what I’ve read, it seems like it affects both approval odds and the interest rate you get, but I’m not sure how much of a difference it really makes in practice.

Is there a big jump between ranges (like 620 vs 700+), or is it more about your overall financial profile?