Hidden Stats can be purchased as a bulk stablewide option in the Pro Shop, which will not only give this to every horse you currently own, but all horses you ever own. These will appear on the horse's page in the Stats section. It will include a number for each stat, a bar with distances, bars for dirt and turf, and a potential. The numerical stats will appear under the colored stars you get from the Traits Expert, which you must have purchased in order to see them.
Each number shows what the current stat for that horse is. If it is bold, it means that stat is maxed out. If a horse has a bolded 4 for Acceleration, that means Acceleration will not improve. If a horse has an unbolded 4 for Acceleration, that means Acceleration can still improve.
The distances will either be red, green, or yellow. Red distances are those which a horse has little or no training on. They will not race well at those distances. Yellow distances are those which a horse has a moderate amount of training on. Horses can race on yellow distances, but may not do as well. Green distances are those which a horse has trained near to their maximum ability. These are the distances they should primarily be raced at. If your horse has never been trained, ALL of its distances will be red. You can use the information given by the Training Advisor to decide what to train them for.
The surfaces will also be either red, green, or yellow. Red means a horse has little or no taste for running on that surface. Green means the horse likes a surface very well, though not all green surfaces are always equal in preference. Yellow means a horse likes a surface somewhat well, but is not going to run at their best there. In many cases, you can still run a horse on yellow surfaces and not see much noticeable difference in performance.
Finally, Potential is a number which tells you the current total of all the stats. If your horse has just been born, it will always have a potential of 6. The potential will go up as a horse gets older (assuming it is trained). A horse with a low potential may or may not be a bad horse in the long run, because it may just need some training to improve. This figure is called Potential because it is just that - a potential estimate of how well your horse may run. Many horses do not run as well as they potentially could, due to other factors in races.
60 is the maximum potential a horse can have! Anything above 40 is typically a strong stakes (G2+) contender, and anything over 50 will usually do well in G1 races. Horses with potentials between 30-40 usually do well in G3. Horses with potentials from 20-30 will do well in Listed, while anything under 20 is best suited for Allowance races. Younger horses, steeplechase/marathon racers, or fillies may do well in a higher grade than potential suggests. Horses with poor Peak, Morale, Courage, or Consistency may not live up to their potential and may need to drop down a grade.
Regarding young horses: Young horses are not yet as developed (trained) as older horses, so they will usually do well in a grade above what is listed here. For example, in May of their 2 year old season, a 2 year old with 35 potential may actually be competitive in the highest grade of races available, even if you wouldn't expect to see a 35 in G1 for older horses. Keep in mind that all horses their age are also still in the learning phase and very few will be maxed out higher. Check Peer Comparison to get a better idea of where your 2 year olds should race.