Vegetative reproduction, also called vegetative cloning, vegetative propagation and vegetative multiplication, is a form of asexual reproduction in plants. This process creates new individuals without production of seeds.
In daylilies, new cultivars are created through sexual reproduction, crossing two parent plants to create genetically unique new individual plants. Once the seed germinates and a new plant gets established, it will reproduce itself vegetatively, through new division of the crown, through rhizomes in some varieties and through proliferations. All new plants derived through any means of vegetative reproduction are genetically identical to the original plant grown from seed. New cultivars are always propogated vegetatively in order to be registered and disseminated.
Daylilies divide at the crown. In the photo below, you can see three examples of new fans emerging from the base of an existing mature fan.