I'm slightly confused about whether multithreading works in Python or not.

I know there has been a lot of questions about this and I've read many of them, but I'm still confused. I know from my own experience and have seen others post their own answers and examples here on StackOverflow that multithreading is indeed possible in Python. So why is it that everyone keep saying that Python is locked by the GIL and that only one thread can run at a time? It clearly does work. Or is there some distinction I'm not getting here?

Many posters/respondents also keep mentioning that threading is limited because it does not make use of multiple cores. But I would say they are still useful because they do work simultaneously and thus get the combined workload done faster. I mean why would there even be a Python thread module otherwise?

Update:

Thanks for all the answers so far. The way I understand it is that multithreading will only run in parallel for some IO tasks, but can only run one at a time for CPU-bound multiple core tasks.

I'm not entirely sure what this means for me in practical terms, so I'll just give an example of the kind of task I'd like to multithread. For instance, let's say I want to loop through a very long list of strings and I want to do some basic string operations on each list item. If I split up the list, send each sublist to be processed by my loop/string code in a new thread, and send the results back in a queue, will these workloads run roughly at the same time? Most importantly will this theoretically speed up the time it takes to run the script?

Another example might be if I can render and save four different pictures using PIL in four different threads, and have this be faster than processing the pictures one by one after each other? I guess this speed-component is what I'm really wondering about rather than what the correct terminology is.

I also know about the multiprocessing module but my main interest right now is for small-to-medium task loads (10-30 secs) and so I think multithreading will be more appropriate because subprocesses can be slow to initiate.