Stringhalt is an involuntary flexion of the hock which can affect one or both hind legs. In Australia and New Zealand there is a form of stringhalt which is related to poisonous plants, but in the UK and America the disease seems random. The cause of stringhalt is unknown but is thought to be neurological.
Signs are actually quite variable, I have recently seen a case in which the stringhalt is NOT seen at walk, but at Trot, and the horse panics whenever she starts. Horses with stringhalt do not always pick up at every stride, but often for 5 or 6 strides in a row, and then be fine. Most cases are at walk, and will improve at faster paces. Some may be so severe that it is unsafe to ride them. In all cases the signs are worse when the horse turns sharply or backs up.
The surgery you have been suggested involves removal of PART (but not all) of the lateral digital extensor tendon, which can be done under a general aneaesthetic, or in some cases under standing sedation (depends on the horse). The horse will need to be box rested for 10 days, with lots of bandages, then gently brought back into work. Some horses respond very well to this treatment but others do not.
I have heard of medical treatment being used, and some centres are using muscle relaxants at very low doses. I have no idea if it works yet.
I don't think that there would be much problem with competitive ability in a horse that has stringhalt, unless you want to do dressage, If you merely want to jump him, or do cross country then there is no point putting him through the surgery. However, I don't see any reason why he won't be able to compete in dressage events if he has the surgery and it is successful. If you have ever been to the races, or watch on TV you will notice that a lot of the horses there have stringhalt, and do very well.
My advice as a vet would be that if you like him, buy him (as long as there is nothing else wrong) but remember that if you do, and he has surgery and it doesn't get better, you took him on knowing the risks, and it's your own responsibility.
Alexa:
I think the website you used must be american, because vets in this country are definitely taught about stringhalt. It's more common here than there, and our UK vet schools teach more equine medecine than in the USA I think. Anyway, it isn't easy to confuse a stringhalt with a shiverer, as shiverers do not do their action only when exercising, they will also do it after their feet are picked up (e.g. farriery) and they have difficulty putting their feet down ....... i.e. they shake the leg as it goes down, like shivering. The tail often will shake too.
I have seen one case which was an atypical shiverer, that is once you picked her foot up she wouldn't put it down for ages, and would hop around. Eventually when she did replace her foot, she shivered. I think though she was distressed about shivering and prefered to hop than put her foot down! There is nothing you can do about a shiverer, and like a stringhalt you'll never see one in a grand prix dressage competition!