A horse is said to have a “hard” mouth when he has developed callouses in the corners of his mouth or dead spots on the bars of his mouth where nerve ending have been damaged. The more callouses or dead spots, the more pain he can take and the harder you will have to pull on him to get the response you want.
A horse that has had harsh treatment either from a severe bit or heavy handed reining techniques is less able to discern the pressure from the bit and does not respond quickly to the pressure cues.
It is recommended by some trainers that a young horse be trained in a bit that puts pressure onto the tongue in the early years more than on the bars, thus saving bar pressure for a more mature horse with more training. His more sophisiticated understanding of pressure will require less bar use and help prevent bar damage.
Some hard-mouth callouses can be recovered by a long, bitless vacation. However, dead spots may never recover.