When the patents for regular drugs expire, other manufacturers can apply to make generic versions. These companies need to submit a little information proving that their product is equivalent to the brand-name drug, but they do not have to repeat all of the human studies to show the drug to be safe and effective.
Human studies are very expensive and time-consuming, and generic medications are less expensive because they do not need all the human studies.
However, because vaccines are biologics (medications made using live cells or organisms, also known as "biopharmaceuticals"), they are regulated under a different set of laws. Under these laws, there is no way for a generic biologic to be approved unless the generic manufacturer completes all of the human studies necessary to approve a brand-new drug.
Because such studies are extremely expensive, it is likely that a generic biologic would not be any less expensive than the brand-name product. Essentially, if a generic biologic were to be approved, it would not really be a generic, but a new and separate drug (that would not be equivalent to the brand-name product).
However, recent legislation has aimed at changing these laws. It is predicted that new laws and regulations will allow generic biologics in the near future.