What does it mean when someone says a horse is "heavy on the forehand"? This is a bit of horse-world jargon. Forehand refers to the front half of the body, so to say a horse is heavy on the forehand means that the horse's weight is primarily on the front half of the horse instead of being even or carried in the hind end.
The "motor" of a horse is located in a horse's muscular hindquarters, and when a horse is heavy on the forehand, that motor is unable to move the horse forward with impulsion or around corners in balanced way. Getting your horse up off the forehand is one of the first steps to creating a winning performance horse.
The picture below shows a horse that's heavy on the forehand and a horse that is up off the forehand. Notice in the first picture that the base of the horse's neck, on the top below theS withers, seems to be the lower point of his back- but in the second picture the horse's shoulders are lifted and the horse appears to be going uphill from the tail to the poll. The horse in the second photo (Which is horse #1 after a year of training and conditioning) is letting his hind end step up under him and propel his body forward.