Dead heading is simply the removal of dead flowers from plants. There are several reasons for doing this - first, many plants will re-bloom  after the first flowers have been removed (thus extending the flowering season),  second, to improve the appearance of the flowering bed and third, to prevent the formation of seeds in the case of 'self-seeding" plants. 

Many spent flower heads can be pinched off with the fingers. Others may require a scissors or a pruner. 

Most annual flowers will benefit from dead heading. When you stop the formation of seeds by removing the flower, the plant has more energy to form flowers.

Most perennials can be dead-headed, including delphinium, coneflower, lupine, salvias, lavender, phlox, shasta daisy and yarrow. Some perennials should not be dead-headed either because they will not re-flower or they remain attractive  with dead flowers intact or with the seedheads that follow the flowers, e.g. astilbe, peony, brunnera and epimedium.

Note that dead-heading is different from a more extensive pruning procedure, called “Chelsea Chop” by British gardeners, in which perennial plants are cut down to about a half their size early in the growing season (late May or early June). Plants treated in this way will be less leggy and they will produce more (albeit, smaller) flowers. Also, you may want to leave some seeds to provide food for birds in the winter. 

Courtesy of NYBG Plant Information Service