This isn't the do-all, end-all guideline, but roughly:
C Shows: Local barn shows, also called schooling shows. No points earned (unless it's for the hosting barn), but there is a judge, places given, etc. Turn out for horse and rider tends to be more relaxed. Colors (jackets/breeches/shirt) are mixed, you'll see some half chaps with paddock boots, maybe some bright schooling helmets. Entry fees/grounds fees/class fees are very reasonable.
B Shows: State/Regionally rated. Riders accumulate points for end of the year awards in whatever organization. Shows are more proper than 'C' shows, but more forgiving than 'A' shows in terms of turnout. (Which probably depends on the organization/area.) Cost is also higher, but not extravagant.
A Shows: Nationally rated, bigger prize money, but also more fees and higher cost per class involved. Horses and riders are both turned out impeccably. Proper colors, tall boots, black helmets, horses braided, hooves polished, etc.
Some of the details (turnout, costs) may also depend on your area. And of course, if anyone has anything else to add to my definitions, feel free to. :)