Corba (Common Object Request Broker Architecture)is a standard maintained by the OMG (Object Management Group - a non-profit standards group)
http://www.omg.org/ There are tools that implement the Corba standard and act as the go between for applications that have pieces on different servers (remote). The client hands a request for information to the Broker without knowing how the broker will get the data. The broker shuttles the request to the server that gets the data from a database etc. The point is that the CORBA Tool knows were and how to get the data.
The good point about this is that you can manipulate the data environment (say swap a DB2 database for an Oracle database) and fix up the alignment in the Corba tool without ever touching the application at all.
It also makes it much easier to hook together data scattered over lots of databases. To the application it just looks like it is talking to one broker.
Well, as usual, Microsoft just did not want to play the same as everyone else - so they created DCOM to do the exact same thing - only with Microsoft standards instead of OMG standards. As you can imagine DCOM works especially well with Microsoft products but handles other sources as well.
CORBA and DCOM are both brokering services.
RMI (Remote Method Invokation) is how to do it without a broker.
JINI is more of a networking tool. It allows Drag and Drop control of complicated networks (I'll stop here because I really don't know much about it).