RMI and CORBA are two methodologys for implementing distributed computing.
RMI (Remote Method Invocation) is pure
java, it allows a java process to assess methods in java classes that are running in a seperate process. The other process can be running under a different version of the jvm and can be running on a seperate machine on the network or even across the internet. It consists of an RMI server which is running and a set of client interface classes that handle communication between the two processes using serialization.
CORBA (Common Object Request Brokering) is similar however, it isn't restricted to java. Any programming language can implement CORBA. It communicates through stubs and skeletons using IIOP.
Hope this helps