A minimum cash balance required by a bank is called a compensating balance
The reason a minimum cash balance is required is because the compensating balance is used to offset the cost incurred by the bank to set up a business loan for when you draw money out or buy something. The reason they have to set up business loans is because all of the money in your bank account is never really all there. They loan your money to other people while you have that money in your account and pay it back to you plus a little extra (the little extra is the interest rate you get on your deposited balance).
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