Classification of difficulty is necessarily somewhat subjective, and depends on flow levels, environmental conditions, and equipment used. However the following scale is quite widely accepted:
Class I: Moving water with small waves but no obstacles.
Class II: Bigger waves but no major obstructions.
Class III: Longer, tougher runs, considerably bigger hydraulics with waves, holes and stronger currents. Requires manouvering, but overall level of danger is minimal.
Class IV: Steeper, longer, and more heavily obstructed rapids requiring exertion, technical manouvering, and some experience (not to mention the presence of guides trained in whitewater rescue).
Class V: Very strong rapids with pour-overs, violent currents, big waves and boulders; major vertical drops and obstructions, and holes powerful enough to forcably flip and hold rafts (and rafters). Requires considerable exertion and carries some risk of injury and loss of equipment in accidents.
Class VI: Unrunable, with significant risks of injury or death, but sometimes attempted by highly trained teams.
Class VII: Cannot be run; no exceptions.