In horses, "broken knees" have nothing to do with damage to the bones in the knee.
The term actually refers to damage to the skin and tissue over the front of the knee which, because it's so thin, often results in permanent scarring and some cases restriction of motion of the joint. It's a blemish that can reduce the value of a horse, because it's often assumed that the horse fell because it was clumsy (not always the case, although I've known some major equine klutzes). The injury is most often caused by a fall onto gravel or hardtop.
It often takes weeks for the injury to heal at all, and it requires hosing and bandaging. Antibiotics are often used these days, and in some cases the horse may have tendon damage that requires surgery.
The most common context for broken knees, though, is in reference to a horse with scars from this kind of injury - a "broken-kneed" horse.