Although it is most often used in the context of HTTP, REST is an architectural design pattern and not a communication protocol. The term was coined by Roy Fielding in his PHD thesis and expands many of the design decisions that went into the HTTP protocol into a more high level architecture. Representational State Transfer (REST) is an architectural style that defines a set of constraints for creating web APIs.
It does not have to be a class but can also be a set of functions that are publicly exposed. The service layer methods itself then implement the application logic and make calls to the databases or models.