The Z stands for Zukunft (German for Future). These cars are supposedly used to show what BMW is capahble of. In case of the Z1, Z8 and the Z9, this is true. The Z3 doesn't have any special gimmicks; it 'just' is a good locking retro styled roadster. Al cars use engines from other models.
The Z1 uses the engine of the 325i, the Z3 can be equipped with all engines of the 3-series (although not all versions are available in every country). The Z8 uses the V8 of the M5. The Z9 is equipped with the V8 diesel engine (found in the 7-series). The Z9 is a real prototype / concept car. The others are all in production.
BMW Z9