A Sha-Dar (plural Sha-Darim) was a person with the rare ability to telepathically communicate with horses, and Sha-Darim were sometimes referred to as Clan-Chiefs of the horses. The only country in which they were known to appear was Algaria, which made sense as Algarian society was mostly based on horses and they also spent years training them. Their abilities included being able to sense what a horse is thinking and being able to communicate with them. In Algaria, a Sha-Dar was hailed as almost royalty and when the person's gift surfaced they were granted instant nobility and riches. Celebrations went on for weeks at the discovery of one.
Notable Sha-Dar included Hettar, who, incidentally, was the adopted son of Cho-Hag, the King of Algaria. His ability gained him the title "Horse Lord" in the prophecy. One of the line of the Rivan King verged on becoming a Sha-Dar, but Polgara blocked him, since most Sha-Dar were too caught up in horses and didn't marry. Hettar's marriage to Adara is a prominent exception to this.
Hettar described their power as simply a part of horses' instinctive herd mind.