Technical Service Bulletin. It's a document that Mazda techs can refer to when a customer comes into the dealership with an issue. The service reps can do a search in their database for certain keywords - in this case, "oil burning", or "low oil" - and they'll get a list of applicable TSBs. Then they'll go through the TSBs to see if there is one related to your issue. If there is, the tech can use it to confirm the diagnosis and then complete the repair, usually with some instructions included in the reference.
Another way to look at it is that a TSB is an acknowledgment that there is a problem, and that the manufacturer has some sort of a solution to that problem. It's different from a recall in many ways, the main one being that a TSB repair is not always covered by warranty. So in your case, if you were out of warranty and you went to the dealership with this issue, they would know exactly how to fix it from the TSB, but you may have to cover the cost of the repair (unless they're feeling generous and they goodwill the repair for you).