Credit Scores are a number, between 300-850, that is used to measure how likely you are to pay back your debts.

In practice having a low credit score is an indicator that you are more likely to not pay your debts, and a high credit score indicates you are very reliable.

In turn lenders like banks and credit card companies will offer better (meaning lower cost) terms to people with high scores because they know it's a low risk of them losing money. They will offer worse terms (more expensive) to people with lower scores to offset the risk the person will not be able to pay them back.

The scores themselves are generated by private companies that don't disclose the math they use to generate them, but we know a little bit. Note that having no 'credit history' doesn't mean a poor score, it means no score. People who have never had any sort of loan or credit card at all have no score.

So to get a score in the first place you need some sort of loan, for example a credit card, and then start buying things and paying it off. The credit card company forwards your history to the credit score company and the credit score company takes note that you are borrowing money (using the credit card) and paying it off on time. This is "Good stuff" and gives you a good credit score.

For the bank question, no, not if you just have a checking account or savings account. BUT your credit score does factor in things like the size of your loans and the age of your accounts. For example if I have a massive car loan, and I pay it on time every month, the payment is a good thing (I'm reliable) but the size of the loan is a bad thing (I might not be able to pay other loans I get, because I already have a big one).

Other factors to consider are - people who look for loans need money and needing money is a good sign someone will have trouble paying loans, it's a Catch-22, but looking for loans will actually hurt your credit score for this reason. This is usually minimal and short-lived but it's important to know.