Cutting a nerve to stop pain. It has been used in many different situations.
On one end of the scale a neurectomy for navicular or similar foot lameness is extreme and results in a loss of sensation in most of the foot, leaving the horse prone to stumbling and other inuries/infections that aren't identified early on.
Can also be used in a much more localised way for some ligament inuries etc.
Nerves once cut can regenerate so it doesn't always solve the problem forever.
From your other post, I am taking it that this is for a ligament injury. I have just had the neurectomy and fasciatomy on my mare's PSD... With this injury, like Ben_and_Jerrys has already said, it is a localised loss of sensation therefore the horse can still feel everything else with the leg. I could write you a thesis on the pros and cons of the opertion, but will try to keep it short
The suspensory ligament is in a small channel so any inflammation will make it too big for it's channel and therefore you get the lameness when it is inflamed. Many acute cases heal very well without the operation, and I know shock wave is very successful too. However, a chronic injury seems to show less success with shockwave and rest, perhaps because the ligament has been inflamed for a while therefore finds it difficult to reduce back to size. The operation opens the fascia, which gives the ligament more room to spread so to speak, and the neurectomy takes any sensation away from that area which then encourages the horse to work the ligament in the normal way.
The pros are that the operation does give the ligament room to inflame a little (or stay a slightly larger size as some do no matter if there is lameness there or not as happened in my case) and it is relatively straight forwards with an expert in this sort of procedure. It also has a very high success rate, my mare was given an 80% chance of returning to her previous dressage career which I thought was pretty good!
The cons are that it is done under a GA therefore is a risky procedure as any GA is for horses. Also, there is still a 20% chance it will not work (my vet said some of this was also down to misdiagnosis) and as Ben_and_Jerrys has also pointed out, the nerve can refuse after a period of time (again, this is a smaller amount, but it does happen!)
In a navicular case, they can no longer feel the hoof... this has other