Deadheading is removing a plant's flowers as they fade. This often encourages annuals, roses, and most perennials to set additional blooms. With azaleas and other spring-blooming shrubs, it won't promote more blooms, but it will make the plants look neater. The purpose of a flower (from the plant's perspective) is to attract pollinators that will help the plant create seeds. When a flower is successfully pollinated, it wilts, sending chemical signals to the rest of the plant to slow down blooming and put more energy into developing seeds.
Removing the flowers as they fade interrupts the chemical signals sent by the developing seeds, and the plant usually tries to bloom again. Most perennials benefit from deadheading as their flowers fade. Cut the whole flower stem near the base of the plant when it is finished blooming. The flower stem won't bloom again, but the plant may send up new flower stalks. Newer annual cultivars bloom longer than the old-fashioned ones, but all of them will bloom longer and look tidier if deadheaded. Pinch out or cut off the flower stems as the flowers begin to fade. It's not necessary to wait until all the blooms on the stalk are completely brown to do this.