Literally, "I've got a blank check." means that you have a check that has no amount written on it. In this case it means you are able to purchase a good or service for any amount of money. Seller: "How much are you planning to pay to buy these computers?" Buyer: "It doesn't matter. I've got a blank check."

It means you are able to do something freely without any restrictions. For instance: "I've got a blank check for rearranging my room." means the same as "I can rearrange my room how I like."