Marbling is a recent (last fifteen years) development in controlling heat in mares. They literally put a glass ball in the mare's womb right after ovulation. The mare's system mistakes the ball for an early pregnancy and the animal stops ovulating.
It's not a permanent solution - often the marble is eventually passed by the mare and it only lasts for that year - once the mare goes through winter anestrus she'll start cycling again, and generally it's only reliable for 60 to 90 days - although that can be the length of the show season in some disciplines/ And it can cause uterine infection. However, it's useful if you have a competition mare who's hard to handle when in heat, and once the marble is removed they immediately return to normal cycling and fertility. It only seems to work in about 40% of mares.