Plain English Meaning
A helicopter built and certified to the strictest set of FAA rules, normally because it is intended to carry passengers or cargo for hire. The rules come in two levels: Category A is the tougher one, where the helicopter must be able to keep flying safely even if an engine fails. Category B is less strict and may require the helicopter to land if an engine quits.
Full Definition
A category of helicopter certificated to the highest civil rotorcraft standards under 14 CFR Part 29, designed and built for passenger or cargo transport. Transport Category Rotorcraft are divided into Category A (multi-engine, with engine isolation, performance, and one-engine-inoperative requirements that allow continued safe flight after an engine failure) and Category B (single- or multi-engine, with less demanding performance requirements and no guaranteed ability to flight after engine failure).