It would help to see the record and the exact wording and context. It may mean that Letters Testimentary were issued to someone at the bank to serve as executor of the estate. Or if the deceased was intestate, It may mean that Letters of Administration were issued to someone at the bank to serve as administrator of the estate. Or perhaps there was a trust set up and the bank served as trustee. Or something else. The answer depends on what you're looking at and the exact wording.
But I would guess that the will named the bank or someone at the bank to serve as executor, and Letters were issued by the probate court based on that.