Conformation is how a horse is built, and for dressage you look at it for two practical reasons: whether the shape will make the work easier, and whether it will help the horse stay sound doing that work for years.
You do not need a veterinary degree to form a useful impression. Stand back and look at the whole horse, square, from the side. The most useful single thing to see is an uphill balance: the withers level with or higher than the croup, and the neck coming out of the shoulder high rather than low. Dressage is all about shifting weight onto the hindquarters, and a horse built slightly uphill starts every stride with the odds in its favour. A horse built downhill can still do good work, but it is always fighting its own balance, and the harder the work gets, the more that costs.
Then look at the parts that do the heavy lifting. The hindquarter and hind legs matter most, because collection happens behind. Most buyers are seduced by a flashy front leg and forget to watch the hind end, which is where the career is actually decided. A strong, well-connected back and loin, correct legs, and good feet round out the picture. Small imperfections are normal and rarely fatal. What you are watching for are faults that concentrate strain on a joint, because those are the ones that wear a horse out early.
Movement is the other half. A dressage horse is judged on three gaits, and here is a piece of advice that runs against every buyer’s instinct: the walk and the canter matter more than the trot. The trot is what sells horses in videos, all suspension and knee action, and it is also the gait training can most improve. The walk and canter are much harder to fix. A pure, marching walk with plenty of overstep is worth more than it looks, and a poor walk is close to unfixable. An uphill, balanced canter with an active hind leg is what the upper levels are won on. When you watch a horse move, force yourself to ignore the front legs for a full circle and watch the hind legs and the back instead. If the movement still looks good, it is good.
Above all, watch a spectacular young trot with a little suspicion. A huge floating trot at five can hide a hind leg that cannot collect, and the problem only shows up later when the real work begins. The question is never how impressive the horse looks going past a camera. It is whether it can sit and carry, which is a quieter thing to see and a more important one.