"Carolina style" means: A North Carolinan style of serving hot dogs and hamburgers, involving chili, slaw, onions, and sometimes mustard.. This is a fairly neutral word with no inherent risk attached. There is no real cause for parental concern; it is descriptive vocabulary rather than something dangerous. If your child uses it, context will usually make the meaning clear. A brief, curious question about where they heard it is generally enough to know whether to follow up.