MIDI (Musical Instrument Digital Interface) is basically a way for digital instruments (like your keyboard) to talk to computers, but it can also do much more than that. What happens is when you hit a key on the keyboard, it sends information down the midi out cable. This information isn't acually the sound that you hear, but information about what you just did. eg - At this time (midi has a time code), you hit this key, this hard, and held it for this long. Using this information your computer can record what you actually did in the performance, not the actual sound of it.
If you want to start playing with midi, you'll need midi sequencing software. Also you'll need a cable to go from the midi in/outs on your keyboard to your computer. Most joystick ports on a computer also double as midi ports. I've got a cable with midi in out (round din plugs) one end and a joystick plug on the other end.
With software, you can hit record and play something on the keyboard. The computer stores the data. When you hit play the data is sent back to your keyboard via the midi in plug, your keyboard uses this to play back what you recorded. You can also do other cool things using the sequencing software - eg, say one note is not quite in time with the rest. You can just open up a score of the recording, and move that note to the correct place.
Thats a basic overview, hope it helps a bit.