A kōan or in Chinese a gong'an (公案, lit. "public case") amounts to a literary device for penetrating through the conditioned world, especially, when it comes to words and concepts which act as a huge barrier when we try to see our true unconditioned nature. The problem with koans is that more than often the cure they promise only compounds the disease. The disease I am talking about is knowing only phenomena—not seeing the noumenon, that is, reading words with their attendant concepts, not realizing this is like a finger pointing to the moon—not the moon (noumenon).
An improvement that shortly followed the koan was the huatou (話頭) meaning literally "word-head" which I hasten to add, has to be taken in a spiritual sense. The huatou refers to the ultimate essence or first principle which is also our true nature (pure Mind, unconditioned Mind, etc.). It is beyond (頭) words (話). This, in a way means also, beyond the finger pointing to the moon.
There are many huatous such as, "If all things are reducible to the One what is the One reducible to?" "Who moves this body around?" "What were you before you were born?" Who repeats the Buddha's name?" "What moves my hands and feet?" "What is beyond birth and death?" "Who says I?"
Each and every question—in fact, each thought in our noggin, comes from a mysterious source and disappears back into that same mysterious source from which it arose. If these questions are like ripples of water on the Buddha's clear pond then they come from the water, itself, and return to it. Before the ripples is the hua (頭), the unmoved, un-rippled pure water. All of the huatous just mentioned demands that we connect directly with this unborn self, this pure Mind.
We can also think of the huatou in regard to our Buddha-nature. What is it? Is this nature beyond conceptualization? If so, where is it right now in our mind? If this Buddha-nature is empty of all characteristics, removing all of characteristics from our mind, can we see it right now and if not, why not? What we seem always to fail to see is that, primordially, we are this nature. Having said that, our real problem is that we have no idea what this nature looks like try as we might. Because of this ignorance we latch on to the conditioned being carried away by samsara. With the huatou we are being asked to identify our true nature, exactly, to come face to face with it. If we are lucky we have a teacher and fellow students who are pushing us, making sure we are working on our huatou, not wasting our time. The old teacher might ask us, "When you sit in zazen, who is breathing? Who draws in the breath? Who exhales? I want you to find this fellow."