If you would like to use your computer to tell a stand alone synthesizer keyboard to trigger some of it's sounds you would set up a little network between the two. Just like the Internet. But this little music-only network is called a midi setup. And midi is the language used by these machines to talk to each other. That should make everything pretty clear.
Midi gives you the ability to hook up 16 machines (sometimes more) together and have them send each other all sorts of messages and commands. A typical setup might include a computer, a controller keyboard, a drum machine and a synth module.

A midi cable connects the controller to the computer. Another midi cable goes from the computer to the drum machine, one more midi cable gets pulgged between the drum machine and the synth module.

In this setup the computer sits in between the controller keyboard and the rest of the gear. You hit a key and a "note on" message gets sent through the computer to a specific piece of gear. The reason everything passes through the computer is that the computer becomes what is called a "sequencer".

A sequencer is a machine that lets you play (record) a bunch of notes into it and then have it play them back to you. Along with that basic definition comes a host of other fun abilities that let you edit and manipulate what you recorded. So with the right software a computer becomes a powerful sequencer. Some computer sequencer setups can have hundreds of machines hooked up to a single desktop computer using multiple midi interfaces.

You can decide which machine gets what message by using "channels". On any properly midi equipped machine you have the ability to set the machine to send its messages on any 1 of 16 channels (or even all of them at once).

In our typical setup the controller keyboard is used to enter the notes into the computer so you set it to channel one and it probably will never change. The computer is set to receive messages on channel one so it reads the messages that you can send from the controller keyboard. In the computer you can use a program to redirect that message to another channel. Your computer is connected to the drum machine using a midi cable. The drum machine is set to receive on channel 1. Now, the computer has a program running on it that makes incoming messages on channel one stay on channel one and sends them out through the cable that connects the computer to the drum machine. Since the drum machine is set to channel one it will read these messages and do something. That's pretty much it for the basics of midi. Everything else is just more of the same.

The cable that comes from the computer gets connected to a plug on the back on the drum machine labeled "midi in". Beside it is usually at least one more plug labeled either "through" or "out/through". To this plug you connect a cable that also goes to the "midi in" plug of the synthesizer module. Now you set the synthesizer module to receive on channel 2. Back to the computer. You can use the program running on the computer to make the messages coming in on channel one and send them back out on channel 2. The program sends these messages through the cable that connects the computer to the drum machine the drum machines not only ignores the message but automatically (and always) fires them back out to the "through" plug. These message now travel to the synthesizer module. Since it is set to receive on channel 2 it reads the messages and does something.

The synth module should also have a "through" plug and you can daisy chain up to 32 machines. You could put 16 people with 16 controllers on one side going into the computer and 16 machines on the other end. Each player can control a machine. The computer in the middle would also allow these players to change the machines they want to control. With the right software the computer can allow for a mind-boggling number of ways to redirect and edit all these messages.

This is where sequencing programs come in to play. In our typical setup the computer is running a program called a sequencer. This program allows you to record a bunch of notes you hit on the controller keyboard and put that on a "track". Think of it like a tape recorder track or a piano roll. You can then play the track back, have it loop and play forever. You set the sequencer so that when you play the sequencer, the message on this track get sent out to the cable to the drum machine on channel 1. Then you can go to a new track and set it to send on channel 2. When you click play on the sequencer you can also hit record again but this time you would set the sequencer so it puts the messages coming in from the controller keyboard on the new track (2).

When you stop the "sequence" the notes get saved to the track 2. Since track 2 is set to send messages on channel 2, when you click play the next time around, the sequencer would send the messages on both tracks at the same time to the cable going to the drum machine. The drum machine would read all messages on channel 1, re-send all messages on all channels to the cable that goes to the synth module. The synth module would then read all messages on channel 2. Now you would have what is called a proper multitrack sequence running on your computer. This concludes this section.