I was on a horse forum recently and somebody had asked about the licking-and-chewing motion that horses often display after they learn something or when they are relaxed. There were lots of opinions, some thinking it was a sign that the was horse 'reassuring himself' while others called it the sign of information processing. I love looking at the science behind a thing, so I did some research. Some of the following is still theoretical, but here is a summary of the most logical scientific explanation I could find.
The licking-and-chewing response in horses is closely linked to the parasympathetic nervous system, controlled by the hypothalamus. This is the part of the autonomic nervous system which deals with automatic body functions during a relaxed state, as opposed to the sympathetic nervous system which triggers functions seen in the 'fight or flight' state (as seen below). For example: You shouldn't exercise your horse just after he has eaten because the body cannot efficiently supply nutrients to the muscles for exercising at the same time as fuelling the digestive system, HOWEVER, when the horse's SNS kicks in, it inhibits digestive activity so that his body WILL be able to fuel the muscles (enabling him to flee from danger if necessary).
So both the SNS and the PNS inhibit and stimulate different organ processes to either relax or excite them respectively. When the horse is in sympathetic state, salivation is inhibited, but during the transition back to parasympathetic state, salivation is re-stimulated, resulting in the licking and chewing response. This is not to say that the horse constantly licks and chews when he is relaxed, but when he is coming 'down off adrenaline' or out of sympathetic state, the stimulation of salivation is more acute.
The reason that licking and chewing is often thought to be a response of thought processing during learning (which is not entirely untrue) may be that the learning process has a particular relationship to licking and chewing. Here is an example of a learning process in which the pressure-and-release technique is used:
A Thought for the Horse... : Licking and Chewing; What Does It Really Mean?