Much simpler answer:
Kernel Re-Entrance
If the kernel is not re-entrant, a process can only be suspended while it is in user mode. Although it could be suspended in kernel mode, that would still block kernel mode execution on all other processes. The reason for this is that all kernel threads share the same memory. If execution would jump between them arbitrarily, corruption might occur.
A re-entrant kernel enables processes (or, to be more precise, their corresponding kernel threads) to give away the CPU while in kernel mode. They do not hinder other processes from also entering kernel mode. A typical use case is IO wait. The process wants to read a file. It calls a kernel function for this. Inside the kernel function, the disk controller is asked for the data. Getting the data will take some time and the function is blocked during that time. With a re-entrant kernel, the scheduler will assign the CPU to another process (kernel thread) until an interrupt from the disk controller indicates that the data is available and our thread can be resumed. This process can still access IO (which needs kernel functions), like user input. The system stays responsive and CPU time waste due to IO wait is reduced.
This is pretty much standard for today's desktop operating systems.
Kernel pre-emption
Kernel pre-emption does not help in the overall throughput of the system. Instead, it seeks for better responsiveness.
The idea here is that normally kernel functions are only interrupted by hardware causes: Either external interrupts, or IO wait cases, where it voluntarily gives away control to the scheduler. A pre-emptive kernel instead also interrupts and suspends kernel functions just like it would interrupt processes in user mode. The system is more responsive, as processes e.g. handling mouse input, are woken up even while heavy work is done inside the kernel.
Pre-emption on kernel level makes things harder for the kernel developer: The kernel function cannot be suspended only voluntarily or by interrupt handlers (which are somewhat a controlled environment), but also by any other process due to the scheduler. Care has to be taken to e.g. avoid deadlocks: A thread locks resource A but needing resource B is interrupted by another thread which locks resource B, but then needs resource A.
Take my explanation of pre-emption with a grain of salt. I'm happy for any corrections.
All Unix kernels are reentrant. This means that several processes may be executing in Kernel Mode at the same time. Of course, on uniprocessor systems, only one process can progress, but many can be blocked in Kernel Mode when waiting for the CPU or the completion of some I/O operation. For instance, after issuing a read to a disk on behalf of a process, the kernel lets the disk controller handle it and resumes executing other processes. An interrupt notifies the kernel when the device has satisfied the read, so the former process can resume the execution.
One way to provide reentrancy is to write functions so that they modify only local variables and do not alter global data structures. Such functions are called reentrant functions . But a reentrant kernel is not limited only to such reentrant functions (although that is how some real-time kernels are implemented). Instead, the kernel can include nonreentrant functions and use locking mechanisms to ensure that only one process can execute a nonreentrant function at a time.
If a hardware interrupt occurs, a reentrant kernel is able to suspend the current running process even if that process is in Kernel Mode. This capability is very important, because it improves the throughput of the device controllers that issue interrupts. Once a device has issued an interrupt, it waits until the CPU acknowledges it. If the kernel is able to answer quickly, the device controller will be able to perform other tasks while the CPU handles the interrupt.
Now let's look at kernel reentrancy and its impact on the organization of the kernel. A kernel control path denotes the sequence of instructions executed by the kernel to handle a system call, an exception, or an interrupt.
In the simplest case, the CPU executes a kernel control path sequentially from the first instruction to the last. When one of the following events occurs, however, the CPU interleaves the kernel control paths :
A process executing in User Mode invokes a system call, and the corresponding kernel control path verifies that the request cannot be satisfied immediately; it then invokes the scheduler to select a new process to run. As a result, a process switch occurs. The first kernel control path is left unfinished, and the CPU resumes the execution of some other kernel control path. In this case, the two control paths are executed on behalf of two different processes.
The CPU detects an exception-for example, access to a page not present in RAM-while running a kernel control path. The first control path is suspended, and the CPU starts the execution of a suitable procedure. In our example, this type of procedure can allocate a new page for the process and read its contents from disk. When the procedure terminates, the first control path can be resumed. In this case, the two control paths are executed on behalf of the same process.
A hardware interrupt occurs while the CPU is running a kernel control path with the interrupts enabled. The first kernel control path is left unfinished, and the CPU starts processing another kernel control path to handle the interrupt. The first kernel control path resumes when the interrupt handler terminates. In this case, the two kernel control paths run in the execution context of the same process, and the total system CPU time is accounted to it. However, the interrupt handler doesn't necessarily operate on behalf of the process.
An interrupt occurs while the CPU is running with kernel preemption enabled, and a higher priority process is runnable. In this case, the first kernel control path is left unfinished, and the CPU resumes executing another kernel control path on behalf of the higher priority process. This occurs only if the kernel has been compiled with kernel preemption support.
These information available on http://jno.glas.net/data/prog_books/lin_kern_2.6/0596005652/understandlk-CHP-1-SECT-6.html
More On http://linux.omnipotent.net/article.php?article_id=12496&page=-1
A reentrant function is one that can be used by more than one task concurrently without fear of data corruption. Conversely, a non-reentrant function is one that cannot be shared by more than one task unless mutual exclusion to the function is ensured either by using a semaphore or by disabling interrupts during critical sections of code. A reentrant function can be interrupted at any time and resumed at a later time without loss of data. Reentrant functions either use local variables or protect their data when global variables are used.
A reentrant function:
Does not hold static data over successive calls
Does not return a pointer to static data; all data is provided by the caller of the function
Uses local data or ensures protection of global data by making a local copy of it
Must not call any non-reentrant functions
The kernel is the core part of an operating system that interfaces directly with the hardware and schedules processes to run.
Processes call kernel functions to perform tasks such as accessing hardware or starting new processes. For certain periods of time, therefore, a process will be executing kernel code. A kernel is called reentrant if more than one process can be executing kernel code at the same time. "At the same time" can mean either that two processes are actually executing kernel code concurrently (on a multiprocessor system) or that one process has been interrupted while it is executing kernel code (because it is waiting for hardware to respond, for instance) and that another process that has been scheduled to run has also called into the kernel.
A reentrant kernel provides better performance because there is no contention for the kernel. A kernel that is not reentrant needs to use a lock to make sure that no two processes are executing kernel code at the same time.