"That horse is lame." Modern riders may also say a horse is "off."
A lame horse is one that is showing sign of pain when it moves, either with or without a rider. This can mean limping, or it can mean a much more subtle unevenness of stride. Experienced horsemen can tell instantly if the horse they are riding is lame.
A horse may be "trotted up" to assess lameness. If a horse has a sore front leg, it will drop its head when the opposite leg touches the ground. In the back, a much less prominent dropping of the hip is visible.
A good horseman will not continue to ride a lame horse (outside of some sort of life and death emergency) - both out of concern that the animal is in pain and because they may make the injury, whatever it is, worse.
Lameness is a symptom, not a diagnosis - I'll talk about the most common causes next week. Some can be fixed on the spot, others are far more serious.
I'll also talk about another term you might hear - "bridle lameness."