While most of the major families of Westeros trace their lineage to a time when they were sovereign kings of their specific regions, the Tyrells were actually only stewards to the now defunct House Gardener, which once ruled over Highgarden. The House was promoted to major-status by the Targaryens after the Tyrells surrendered the seat during the dragon lords' initial conquest of Westeros.
The Tyrells remained loyal to the Targaryens during Robert's rebellion, but eventually bent the knee to the new king when he took the throne. The leader of the Tyrells is Mace, but in the first season the most notable member of the family is Ser Loras, who though he is Mace's third son, is the most beautiful and talented warrior, referred to as the Knight of Flowers, on account of his family's sigil. In the books, Loras and Renly Baratheon are depicted merely as extremely close, committed friends, but the HBO series went whole-hog, showing them as lovers.