The Dothraki are the horse lords of the east, a savage people whose customs are very different from those of the people of Westeros. They prize horses and strength, and ride in khalasars behind khals, who are their kings.
Daenerys Targaryen's POV chapters in A Game of Thrones, and a few chapters in A Clash of Kings, take place in their world. In these she marries Khal Drogo, a powerful leader of the Dothraki. However, he dies of a wound gone bad. Daenerys then leads her own khalasar through the Dothraki Sea to a fresh world in her quest to win the Iron Throne.