A 'proven' horse, be it a mare or stallion, has either won at competitions or work and/or has produced foals that have gone on to do well in whatever sphere was chosen for them
I think for many people a proven broodmare or stallion is one who has reproduced successfully.
To me it is a stallion or mare that has offspring as good or better than themselves, repeatedly.
This is just in the reproductive context. If you were talking about the whole animal being 'proven', they would have to prove themselves in the show ring, as well as the breeding shed. For example my BO's old mare. Successful on the track, excellent mountain horse, winning endurance horse, and every foal is as good or better than her self.
To me a stallion or broodmare doesn't necessarily have to prove themselves in the show ring, if their offspring are truly exceptional. For example a stallion I used to work with. Amazing temperament and breeding, was injured in the pasture as a yearling and couldn't stay sound on the track long enough to race, so was retired to breed. Every foal was spectacular, he had several thoroughbred foals that not only raced successfully, but went on to be excellent saddle horses, a andalusian cross that excelled at dressage, several draft crosses that went on to pull carriages and event, and others. Every foal was useful, good tempered, and as good or better than himself. He was a proven stallion.