Ah yes, you mean a DI (Direct Input) unit/box. They are used for things that do not have "balanced" outputs such as keyboards and some amplifiers, as these would damage PA equipment if plugged straight in.
(Warning - this may turn into a general PA post...)
The fact that you could not hear yourself could be due to a number of things. Check the volume level on your keyboard and the "level" and "gain" settings on the mixer. The gain should not need to be very high, but experiment (carefully!) with the levels on the mixer and the keyboard. If neither of these work, see if the DI you are using has a ground lift - that might be affecting the sound.
PA systems are complex beasts and are usually use for live sound where the audience and the musicians need to hear what is going on. Monitor speakers are used so that the band can hear what they are playing and are normally pointing at the band from the front of the stage (headphones/earpieces are sometimes used) and then the speakers for the audience are much bigger and facing them.
I would guess your system would look a bit like this:
You --> Keyboard --> DI --> mixing desk --> house speakers
|-->band monitors
In this case the desk operator controls what the band hear and how loudly they hear it. It may be that your system does not have monitors, in which case you will just be using the house speakers. This is fine for rehearsal, although you do not have any control over how loud you hear yourself - keyboards often get lost in the mix.
This post is long enough as it is, but feel free to ask more questions!
I think that Mourndark has it mostly right, except that I wouldn't worry about wrecking a PA without a DI box.
Without going into two much detail, there are essentially three strength levels of sound signals, microphone, instrument, and line level.
Line level is the standard signal level that is used in all professional mixing consoles and most rack effects.
Microphone and instrument level signals need to be amplified before they can be "heard" by most equipment. Most mixers or PA desks have preamplifiers for microphones, but not for instruments, and this is where the DI box comes in.
All the DI box does is take low level signals (like those out of instruments) and change it into a line level signal for the mixer.
The DI box allows you to plug your keyboard into the mixer and be heard. Now the reason for not hearing yourself could be a number of things, the sound engineer might have had your monitor level really low, there might not have been any stage monitoring at all, or there was a cable problem between the mixer and the monitor, or your keyboard volume could have been too low between keys and the DI box.
Ways to remedy this would be to get the sound engineer to play with the monitor level until you like what you hear, or to get a splitter and a small amplifier so that you can send one signal to the DI box (and on to the PA), and another to the amplifier so you can adjust the stage volume as you like.
