Basically, enemy ships with a word floating over them will appear on the top part of the screen. To destroy them you must type in the exact word, a task which will seem easy at first but which will turn quite frantic once you reach the fiftieth wave.
Having said this, the truth is that if you know how to type relatively fast then the game will be quite boring at first, as you'll find very little opposition and you'll destroy your enemies even before they appear.
All in all, Z Type is a fun game which can help you improve your typing speed. Beware however, as it can be quite addictive.