For some web article:
"Big Brown went off as the 3-10 favorite in the Belmont. He was rank in the early stages of the race, and nearly ran up on the heels of eventual winner Da' Tara."
What is "run up on the heels"?
not a teacher
As with a human foot, the back of a horse's hoof is called the heel.
Big Brown ran so close to the horse Da' Tara in front of it, that Big Brown's hooves nearly touched or hit Da' Tara's heels.