It isn't that the condition variable will erroneously wake up; the condition variable will only wake up if it has been signalled from another thread. However, it is possible that by the time the thread has been re-scheduled for execution, some other thread has already managed to nab the resource on which you were waiting, and so it is necessary to double-check. For example, if a group of threads x,y,z are waiting on some resource R that w was previously holding, and x,y,z,w communicate through a condition variable... suppose w is done with R and signals x,y,z. So, x,y, and z will all be taken off of the wait queue and placed in the runqueue to be scheduled for execution. Suppose x is scheduled first... so then it acquires R, and then it might be put to sleep, and then y might be scheduled, and so when y is running, the resource R on which y was previously waiting is still not available, so it is necessary for y to go to sleep again. Then z wakes up, and z also finds that R is still in use, so z needs to go back to sleep again, etc.
If you have exactly two threads, and the condition variable is shared between just the two of them, there are sometimes situations where it is ok to not perform that check. However, if you want to make your application dynamic and capable of scaling up to an arbitrary number of threads, then it's good to be in the habit (not to mention much simpler and less worrisome) to do that extra check as it is required in most situations.