What does the remark description indicate on a Non-Resident Non-O visa issued by a Thai embassy?

There can be some issues opening bank accounts especially in more rural areas, a friend of mine could only open an account with a house book in his name, they wouldn't even accept a residency certificate but he was in a very rural area with very few expats so the bank was probably just working on what is necessary for a Thai. It also varies between banks & branches, I had trouble in the Kasikorn branch in Central Khon Kaen but no problems at the Lotus branch, both time I had a residency certificate. If one bank/branch gives problems even with the residency certificate then try another as it's common to get different 'interpretations' of the rules.