RMI is Remote method Invokation. In terms of disributed computing you can use this to remotely invoke a method from your PC and that method exists on another PC on the Network. This you maybe thinking ok whats the point, but You are taking object-orientation to another level. here you are segregating a task within a method to a dedicated PC or server.

Say for instance you have a game, and the GUI and diplay stuff is on the client machine in the form of an Applet via web browser. Now say for example the game uses ANN (Artifical Neural Networks) this is very computationally time consuming, and will take ages on any average PC. Now as a deveoper you would want this game to be fast as possible, one apprach is to distribute computing, so you dedicate all of the ANN computing in a Class on a fast remote server. These methods can be Invoked via your client machine, Thus making an overall faster system. This can be done in few lines of code unlike other languages.

Please refer to the sun micro systems site. Thers loads of material every where.
Java is such a big language, I would love to tell you more, but I have a Server OS to build.

take care