As you have observed it does nothing in the default implementation. The function seems to be a placeholder for checking whether a particular thread holds a mutex and optionally abort if it doesn't. This would be equivalent to the normal asserts we use for variables but applied on mutexes.
I think the reason it is not implemented yet is we don't have an equivalent light weight function to assert whether a thread holds a lock in pthread_mutex_t used in the default implementation. Some platforms which has that capability could fill this implementation as part of porting process. Searching online I did find some implementation for this function in the windows port of leveldb. I can see one way to implement it using a wrapper class over pthread_mutex_t and setting some sort of a thread id variable to indicate which thread(s) currently holds the mutex, but it will have to be carefully implemented given the race conditions that can arise.