The red part that sticks out on the top of the rooster's head is called its comb, and the part dangling beneath its chin is called its wattle. Researchers have found that the brightness of the rooster's comb has an effect on his desirability among hens when selecting a mate.
Researchers also believe that the brightness of the comb is indicative of the health of the rooster. The wattle is used to attract the attention of hens, and the bigger it is, the more attractive it becomes. It is not really the wattle itself that the hens care about, but it is used instead by the rooster to advertise that he's willing to share his food with the hen.