Since each thread has its own stack, its private data can be put on it. For example, each thread can allocate some heap memory to hold some data structure, and use the same interface to manipulate it. Then why thread-specific data is helpful?
The only case that I can think of is that, each thread may have many kinds of private data. If we need to access the private data in any function called within that thread, we need to pass the data as arguments to all those functions, which is boring and error-prone.
Unlike the stack (which, like thread-local data is dedicated to each thread), thread-local data is useful because it persists through function calls (unlike stack data which may already be overwritten if used out of its function).
The alternative would be to use adjacent pieces of global data dedicated to each thread, but that has some performance implications when the CPU caches are concerned. Since different threads are likely to run on different cores, such “sharing” of a global piece of data may bring some undesirable performance degradation because an access from one core may invalidate the cache-line of another, with the latter contributing to more inter-core traffic to ensure cache consistency.
In contrast, working with thread-local data should conceptually not involve messing up with the cache of other cores.