Your credit score can have an effect in two ways: Whether you can get approved for a financial product in the first place, and what interest rates you may have to pay if you are approved. The higher your FICO score the more likely you are to get approved for a credit card or loan, and will usually reduce the interest rate associated with that particular loan or card. Lower scores may disqualify you for a product or service completely and can raise your interest rates significantly otherwise.
For many credit cards, especially the most lucrative rewards cards, the cards are offered only to consumers that meet a minimum credit quality. Many of the best cards are exclusively marketed to consumers with excellent credit scores. When it comes to credit cards your credit score can determine the breadth of options you can choose from. Most cards are also marketed with a range of interest rates/APRs. The actual interest rate on your specific card will be inversely related to your credit score with higher creditworthiness receiving lower interest rates and vice versa.
With mortgages and auto loans, lenders behave similarly. Your credit score is used as a component whether or not a bank will choose to approve a loan or may force you to make additional concessions for approval. It can and generally will move the interest rate you pay on the loan as well.