These are flags used for horse racings. Each flag or banner represents a different city ward in Italy. They represent the wards that participate in the horse race that is held to this day. I may be wrong but the horse race is called "The Palio di Siena", held in the city of Siena, Italy in Tuscany. Mr. Hearst thought they were interesting and decided to use them to decorate his dining room.
The Hearst Castle Refectory is very grand, large in scale and filled with rare museum-quality furnishings. The room measures 67 feet long and 27 feet wide. The walls rise 27 feet to an ornate carved wooden ceiling, which originally belonged to a 16th century monastery in northern Italy. The walls of the room are lined with Gothic Flemish tapestries and paneled with 15th century choir stalls from a Cathedral in Spain. Silken Italian flags known as Ward banners, some over 400 years old, hang between the French Gothic windows. An enormous French Gothic fireplace gapes at the end of the room, the largest of 38 fireplaces in the Castle. The dining tables are monastic refectory tables. Pieces of Hearst’s large antique silver collection can be seen throughout the room.
Despite its valuable antique tapestries and museum-like decor, the food served at Hearst Castle was somewhat rustic. Hearst had always envisioned the castle as his “ranch residence,” which meant that the meals were comprised of fine quality comfort-style foods.