While it may have nothing to do with deadheading some of our garden plants will look better after they have flowered by cutting them back several inches to promote fresh new foliage for the rest of the summer. Flowers that tend to open up and fall apart benefit from this kind of care. Speedwell is good example. Some of our garden perennials really die back in the heat of the summer and that dead foliage can also be removed. Poppies would be one of those plants. The foliage really dies off and returns as a fresh rosette later on.
We deadhead to improve the appearance of the flowering plant for the rest of the summer, especially if it is a one-time bloomer. If your flowers re-bloom all summer, then deadheading is a way to clean up the flower and encourage new bud set. We may not worry too much about annuals, yet we should be deadheading our perennials for another good reason – building food reserves for next year. By deadheading you are removing any flowers that later may be setting seed and in doing so use up food reserves. While we love our flowering garden plants, left to go to seed may mean that we will be finding seedlings in unexpected places. If these seedlings are left to grow, the gardens begin to have that unkempt look. A common re-seeder in a perennial bed is coneflower. Unless you know that those spent flowers do not contain viable seed, do not compost them. One consideration for leaving those seed heads will be if you are "birder" and want to at attract wildlife into your yard.
For our spring flowering bulbs, you can also deadhead if you see seed heads forming on flower stems if the flowers were where pollinated. There is also the temptation to cut the remaining foliage to make room for annuals or expanding perennials. Bulb foliage should be left intact until the leaves naturally decline. The bulb foliage is the only way the plant has to replenish the food reserves that allow the bulb to create the flower parts within the bulb for next year.