A common term to describe maxing a skill of one of your horses. It is named due to the text of the skill changing to bold once achieved. It plays a role in what inborn skills a foal gets from its parents, as well as the BLUP.
Bolding is used to increase the BLUP of your horse. The top 3 skills of your horses breed must be maxed out. To see what the skills are, check the Genetics tab below your horse. The top skills have the highest numbers, and is the same for mixed-breed horses.
Each player has his/her own way of training their horses. These tips are from the Howrse UK forums 
As soon as a horse is old enough to do rides, do as many as you can. Remember that short rides are for speed and long for stamina.
Enter competitions when the horse is 3. The more trained a horse is, the harder to win competitions. To ensure easy wins do not train primary skills but the secondary skills.This ensures that you can enter easier competitions and helps towards the 20 wins you need for BLUP. Make sure your horse has full morale and energy when entering competitions. Competitions skills:
Show jumping: Primary: Jumping Secondary: Dressage, Speed
Cross Country: Primary: Stamina Secondary: Dressage, Jumping
Races (Gallop and Trot) Primary: Gallop / Trot Secondary: Dressage, Speed
Dressage Primary: Dressage Secondary: Gallop, Trot (compiled by Manya on the Howrse UK forum)
When your horse no longer gains from training or rides then keep using competitions to increase skills. Lessons are good to increase the top 2 skills your horse has, however, they take up to 30% energy.
The average age that a horse's has Bolded its skills and it has a full BLUP is 15, but some experienced players may be able to do it faster.
Black Market items are useful though it is still possible to train your horse without them.
Beach rides help train your horses top 2 skills but you lose points from your lowest skill. The points are exchanged so that you gain as much as you lose.