Strung out is a phrase used by horse people, judges, riding instructors, and horse trainers to describe a horse that is not moving correctly. Horses that move and use their body correctly not only look better and will place much, much better in horse shows, but horses that carry a rider correctly and use their body well are significantly less likely to become injured or to develop arthritis and joint problems as they age.
“Strung Out” is a phrase with only a general meaning, and may be used along side terms like “heavy on the forehand”, “not tracking up”, “sluggish”, etc.
A horse that is moving strung out is usually heavy on the forehand, hollow in their back, and sort of appear to be dragging themselves forward with their front hooves with their hindquarters sluggishly following.
A horse that is not strung out, on the other hand, will be light on the forehand (carrying most of their weight on their hindquarters), with a rounded rounded back, and stepping deep under themselves thereby using the hindquarters to push the lightened front end forward.
If someone tells you your horse is strung out, this article can give you a basic idea of what that means, but the best way to determine how to improve is to ask that person specifically what about your horse looks strung out.