A class of drugs is a group that have similar characteristics; they may cure the same diseases, have similar chemical structures or work in the same way.
Within each class there will be generic drugs, and brand name drugs. Further, insurers and other payers create their formularies to include different drugs in a class on different tiers.
For example, "antibiotics" are a class of drugs. Each drug is made up of slightly different ingredients, but those ingredients work the same way, and have the same purpose - to kill bacteria in a person's body. Examples of drugs in the class of antibiotics are amoxicillin, Ciprofloxacin, Erythromycin, Tetracycline or others.