When is a condition variable needed, isn't a mutex enough?

Even though you can use them in the way you describe, mutexes weren't designed for use as a notification/synchronization mechanism. They are meant to provide mutually exclusive access to a shared resource. Using mutexes to signal a condition is awkward and I suppose would look something like this (where Thread1 is signaled by Thread2):

Thread1:

while(1) {
    lock(mutex); // Blocks waiting for notification from Thread2
    ... // do work after notification is received
    unlock(mutex); // Tells Thread2 we are done
}

Thread2:

while(1) {
    ... // do the work that precedes notification
    unlock(mutex); // unblocks Thread1
    lock(mutex); // lock the mutex so Thread1 will block again
}

There are several problems with this:

1. Thread2 cannot continue to "do the work that precedes notification" until Thread1 has finished with "work after notification". With this design, Thread2 is not even necessary, that is, why not move "work that precedes" and "work after notification" into the same thread since only one can run at a given time!
2. If Thread2 is not able to preempt Thread1, Thread1 will immediately re-lock the mutex when it repeats the while(1) loop and Thread1 will go about doing the "work after notification" even though there was no notification. This means you must somehow guarantee that Thread2 will lock the mutex before Thread1 does. How do you do that? Maybe force a schedule event by sleeping or by some other OS-specific means but even this is not guaranteed to work depending on timing, your OS, and the scheduling algorithm.

These two problems aren't minor, in fact, they are both major design flaws and latent bugs. The origin of both of these problems is the requirement that a mutex is locked and unlocked within the same thread. So how do you avoid the above problems? Use condition variables!

BTW, if your synchronization needs are really simple, you could use a plain old semaphore which avoids the additional complexity of condition variables.

Mutex is for exclusive access of shared resources, while conditional variable is about waiting for a condition to be true. People may think they can implement conditional variable without the support of kernel. A common solution one might come up with is the "flag + mutex" is like:

lock(mutex)

while (!flag) {
    sleep(100);
}

unlock(mutex)

do_something_on_flag_set();

but it will never work, because you never release the mutex during the waiting, no one else can set the flag in a thread-safe way. This is why we need conditional variable, when you're waiting on a condition variable, the associated mutex is not hold by your thread until it's signaled.

I was thinking about this too and most important information, which I was missing everywhere was that mutex can own (and change) at the time only one thread. So if you have one producer and more consumers, producer would have to wait on mutex to produce. With cond. variable he can produce at any time.