I read that Linux kernel is preemptive, which is different from most Unix kernels. So, what does it really mean for a kernal to be preemptive?
Some analogies or exam
It means that the operating system scheduler is free to suspend the execution of the running processes to give the CPU to another process whenever it wants; the normal way to do this is to give to each process that is waiting for the CPU a "quantum" of CPU time to run. After it has expired the scheduler takes back the control (and the running process cannot avoid this) to give another quantum to another process.
This method is often compared with the cooperative multitasking, in which processes keep the CPU for all the time they need, without being interrupted, and to let other applications run they have to call explicitly some kind of "yield" function; naturally, to avoid giving the feeling of the system being stuck, well-behaved applications will yield the CPU often. Still,if there's a bug in an application (e.g. an infinite loop without yield calls) the whole system will hang, since the CPU is completely kept by the faulty program.
Almost all recent desktop OSes use preemptive multitasking, that, even if it's more expensive in terms of resources, is in general more stable (it's more difficult for a sigle faulty app to hang the whole system, since the OS is always in control). On the other hand, when the resources are tight and the application are expected to be well-behaved, cooperative multitasking is used. Windows 3 was a cooperative multitasking OS; a more recent example can be RockBox, an opensource PMP firmware replacement.