This is the process of removing old flower heads after peak blooming unless the seed heads are ornamentally desireable.
Old flowers on daylilies should be removed so food energy goes into producing more blooms rather than seed formation. In addition, the plant looks better.
Some seed heads are actually very attractive. Don't deadhead Belamcanda chinensis, or commonly called Blackberry Lily, which refers to the blue-black seeds that emerge from the ripened seed pod in September. Deadhead the pods by October 15 or you will have many Blackberry Lilies popping up next year from seed.
Deadheading can prolong flowering of many perennials. Coreopsis always benefits from deadheading, sending up more flowers later in the season. The flowers won't be as prolific as peak bloom, but you will have a longer season of color.
To prevent some perennials from nuisance reseeding, deadhead after their peak bloom. Echineacea (Purple Coneflower) and Rudbeckia (Black-eyed Susan) will reseed if flowers are allowed to mature. If you don't want more of these plants, deadhead after bloom. If you want birds to visit your garden and eat the seeds, realize you will deal with seedlings next year. The choice is yours -- there is no right or wrong way.