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Generally, the logical representation of an entity of the real world. From a developer's perspective, a business object (a.k.a. "domain object") represents a logic entity in a given domain, including attributes, relationships, business rules/logic, policies and constraints.
The business object layer provides an explicit business-oriented domain model as an API. In a picture that shows the typical architecture layers of a business application, it can be located on top of the persistence layer (or data layer), and below the application layer that forms the actual application from a reusable domain layer - the business object layer.
It forms a new level of abstraction over the persistent state of objects. It comes with concepts to change and extend the behavior of business objects without breaking the cartridge API barrier. It hides the underlying internal implementation, which can still be based on the existing ORM model, or on any other back end. It also provides a more object-oriented view on the available business functionality, which, for example, makes user interface development much easier.