This is vague term that is common mostly in working German Shepherd circles, but can be used when referring to any dog. It describes a dog that can think clearly and remain focused when highly stimulated.
In order to understand what clear headed is, it is best to see what a dog that is NOT clear headed is like. These are dogs that can get “worked up” easy in anticipation of stimuli and loss of focus while stimulated that may result in various frantic behavior such as: misdirected bites, hard to control barking or other vocalizations, spinning, jumping, etc..
A good example of a clear headed dog can be relaxed, then work hard and focused when needed, and then calm back down easily.
As in all temperament traits there is a grey area between what is and what is not clear headed.
Dogs that are not clear headed tend to also be prone to barrier frustration.
Here is an example of a dog that is “clear headed”. The dog can stay calm in anticipation of high arousal stay focused during arousal, and shut it off afterward.
Here is a dog that is LESS clear headed. Keep in mind that other factors play a part in a dog’s presentation during training, but in general this dog (although still a very good dog) has a harder time staying focused in anticipation of stimuli.
Like all temperament traits how clear headed a dog is depends on genetics and it isn’t necessarily a good or bad thing depending on the intent of the breeder. For example, a tendency for excitability and barking could be a good thing to someone who breeds for sport work and wants a dog to easily perform a “bark and hold” exercise. A “clear headed” dog may not be as easy to animate in this case when all else in the training plan is equal.