The Object Management Group (OMG) is a consortium of companies that have banded together to develop an object communication standard. The Common Object Request Broker Architecture (CORBA) is a standard that competes with Microsoft's Component Object Model (COM) in many ways.
The various companies involved, and the industry press, tend to dwell on the differences between the two competing standards. While it's true that there are differences, what I want to emphasize here is the similarities between these standards.
Both CORBA and COM provide standardized mechanisms for objects to communicate with each other. They specify how components and applications can be built in a distributed and organized fashion. CORBA, like DCOM, provides for communication between objects distributed across a network, providing for complex multi-tiered applications based on the standard.
Perhaps most importantly, CORBA and COM both encourage the use of business objects in their architectures. And they both advocate a separation of business rules from the presentation layer, in such a way that the main application logic is contained in an object model that's largely independent of the user-interface.