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.

I guess you mean the Non-O visa which is a Non-immigrant visa with the O standin for Other. That visa is never issued for the purpose "Other", it can be issued for 10 or more reasons such as retirement, marriage and so on. Sometimes it will specify the reason sometimes it won't. What's your particular concern?

The Non-O type normally appears as Thai characters in the Remarks field so you'd need someone who can read Thai to translate

On mine is says not permitted to work in Thai