I've used this term a fair bit and just realized I never properly defined it.
A horse's conformation (conFORmation - it's very common to see it typoed to confirmation, making me wonder if people's horses are Catholic) is how the animal is shaped and put together.
Horse people spend a lot of time talking and thinking about conformation. Poor conformation can cause unsoundness, health problems and make an animal less useful, so a big part of horsemanship is choosing horses for work and breeding (especially breeding) that have good conformation. A good horse person can tell if a horse is well put together right away at one glance.