What is meant by CoreData is not thread safe?
@d11wtq's answer is correct only when writing your own code or designing your own APIs.
It is entirely incorrect when working with a set of APIs and quite specifically wrong when working with Core Data.
In the context of working with Mac OS X and iOS, thread safety must always be considered in the context of working with the system APIs. Even using, say, an NSArray means that you are working with the system APIs.
OR in general what is "not thread safe" ?
A non-thread safe API is an API where you cannot interact with the API from multiple threads simultaneously. There may also be additional restrictions that most often involve the main thread. For example, almost all drawing operations must occur on the main thread on both Mac OS X and iOS.
The Apple documentation assumes thread safety is the exceptional case. That is, an API is only thread safe if the documentation explicitly claims thread safety. If there is no mention of thread safety, you must assume that the API is not thread safe.
In Obj-C, what does it mean in simple terms; "CoreData is not thread safe"
That statement is not quite correct, but it is a safe assumption.
In Core Data's case, the thread interaction behavior is extremely well documented.
In short, parts of the API are thread safe (the store coordinator, for example) and parts are quite explicitly not thread safe. While the MOC provides lock and unlock methods, you can also use external locking. But don't. It will be less efficient and more fragile; significantly so. In general, don't use the internal locking either. CoreData is optimized around having a context per thread/queue.
(Answer fixed based on TC's feedback. Thanks.)
UPDATE | Please see @bbum's answer. I accept that my answer is flawed and @bbum is correct.
If something is described as "not thread safe", it means that no special precautions have been taken to ensure it won't crash should two separate threads try to use it simultaneously. In general, code that is to be used by more than one thread requires explicit locks (or @synchronize blocks) wrapping around aspects of the code. In particular, any object/variable that will be modified would almost certainly cause a crash if two threads happened to write to it at the same time (since they'd be writing to the same memory address). Similarly, if one thread was reading a variable while another was writing to it, garbage would be returned and the program would likely crash.
Using @synchronized, or NSLock or a POSIX mutex etc, ensures that only one thread can execute a particular block of code at any given time. The other threads get blocked and have to wait until the lock is released. There is a slight performance hit with using locks (and of course some development overhead having to think about them), so often code expressly declares that it is not thread safe, leaving you, the adopter of the code, to place locks as needed yourself (or limit execution of the non thread-safe to a single thread).
See the Apple documentation for more information about threading and thread safety: