A removable partial denture (RPD) is for a partially edentulous

Edentulism

Edentulism is the condition of being toothless to at least some degree; it is the result of tooth loss. Loss of some teeth results in partial edentulism, while loss of all teeth results in complete edentulism....

 dental patient who desires to have replacement teeth for functional or aesthetic reasons, and who cannot have a bridge

Bridge (dentistry)

A bridge, also known as a fixed partial denture, is a dental restoration used to replace a missing tooth by joining permanently to adjacent teeth or dental implants....

 (a fixed partial denture) for any number of reasons, such as a lack of required teeth to serve as support for a bridge (i.e. distal abutments) or due to financial limitations.

The reason why this type of prosthesis is referred to as a removable partial denture is because patients can remove and reinsert them when required without professional help.