Conformation is directly related to a horse's health and performance. Conformation is SO much more than how nice-looking a horse is.
If a horse has, say, crooked legs, it's not going to stay sound and will be more prone to injuries.
Horses with upright pasterns are more prone to navicular. Horses with long backs have trouble making tight turns, so would be bad for jumpers or barrel racing. A horse with a thin neck will have trouble "rounding" and getting into a proper frame. Horses with sickle hocks have an easier time making sliding stops, but they pay for it with having a difficult time extending their stride. A horse who is built downhill will naturally be a poorer jumper than a horse who is built uphill. The list goes on and on.
Of course no horse has perfect conformation, but some are significantly better than others. There are some flaws that you can live with, and others that will really hurt the horse or make it unsuitable for any serious riding.
Horses may even have to be put down if their conformation is poor enough; a horse with a very severe fault might not be able to live comfortably and could have to be put down, just because of how uncomfortable its life would be otherwise.
I suggest you read the wikipedia article on horse conformation:
http://en.wikipedia.org/wiki/Equine_conformation
It has a lot of good information, as well as some common faults and how that will impact the horse. There's a lot of good books out there on conformation too, but the wikipedia article will probably suit your purposes.
To me, conformation is one of the most important things about a horse (if I intend on riding it and doing some serious sports with it). Good conformation will really increase a horse's price- I have seen horses sell for 50,000 JUST because they have awesome conformation. A horse with very bad conformation will rarely sell for more than $2500, even with all the training, heart, and ability in the world... just because it won't be able to stay sound and healthy.
Conformation doesn't have anything to do with personality/temperament, that's 100% mental. Conformation relates to health, ability to do a sport, and soundness.
ADD-- There are the rare few who are capable of overcoming shoddy conformation and becoming great athletes... just look at Seabiscuit:
http://www.personal.psu.edu/staff/k/a/kah19/seabiscuit.jpg
As cute as he is, Seabiscuit is very over at the knee and has a poorly constructed neck. BUT- Seabiscuit also ruptured a suspensory ligament in one of his front legs... perhaps that injury was tied to his conformation, noone can say for sure but I think it's certainly possibly that his conformation caused his career-threatening injury.