I'm pretty sure this is the treatment that generally gets a lot of cringing when brought up - a lot of you out there are needly-shy and cannot fathom any good reason outside of medical needs to tolerate something stuck into your skin. The important thing to keep in mind is that acupuncture needles are generally SMALL, and their purpose is not to elicit pain of any kind.
A facet of traditional Chinese medicine, acupuncture is thought to help adjust energy flows in the body. This energy is commonly referred to as "chi", and is thought to travel the entire body - again think like a complicated electrical circuit - when a weed or tree branch leans on an electric fence, it causes the fence to "ground out" and the electric pulse returns to the ground through the weed/tree branch, and does not continue to travel through the wire of the fence. In this same light, when the energy flow of the body is disrupted due to sickness, injury, or even general stress, the body has a hard time recovering itself.
Acupuncture enlists the use of needles at certain pressure points to help properly establish the Chi, and restore the body to its normal settings. In doing so it can help relieve stress and reduce muscle strain. Sometimes injections are given at these points - the most common being vitamin B 12. Other times the needles are given a slight pulsing current (this is called Electro-accupuncture) to stimulate the Chi. Again back to my personal experience - my horse had this done to "energize his hind end". Afterwards I had a week of a violently cheerful, explosive, bucking monster. I'd certainly say energize was the correct term for its effect.
Oftentimes I find that a chiropractor will make use of acupuncture before or after an adjustment. Again, it is important to remember at all times that the body has a memory - when it gets used to a certain position or compensation, sometimes just alleviating the cause is not enough to fully restore the animal. Especially because we cannot TELL our animals: "we fixed the problem, and now you will not hurt anymore." and they generally do not have the perseverance to work past pain - if it hurts them to do something, they will not risk doing it again. They find ways to cover, or resist. Acupuncture can often help to relax a horse who is too tense to adjust.
On its own, as already stated, it can also help restore that energy flow, and make the animal more willing to recognize their pain is gone, and test out their body. Unlike most drugs, it will not make them blind to pain that is still present. It will instead help them to manage and deal with it, and recognize when it is truly gone.
As with any veterinary visit, it is important to have someone present that can give the practitioner a full history - not only of symptoms, but of the horse's work schedule, personality quirks, etc. While the horse's body can sometimes tell its own version of what's going on, it helps to have multiple sides of that story. It can also offer valuable information on the horse to its owner/rider/trainer because it can explain why the horse is having certain difficulties. It can overcome a language barrier and bring to light the root of a certain issue, and once revealed that issue can be properly dealt with. It can even pinpoint certain weak points that are likely to cause problems in the future!
For more information, you may find this website helpful:
Acupuncture for Horses
Modern Acupuncture for our Equine Friends