"A proliferation is a leafy shoot from a node or bract found on scapes of many cultivars. Small roots often form and occasionally a flower is produced while the proliferation is still on the scape. (Definition from the American Daylily Society.)
For those of you who are unfamiliar with daylilies, their seeds are not identical to either parent plant. A proliferation is one way to get an exact replica of the plant you have (in addition to plant division). I have had good results growing daylilies from proliferations. In fact, I have huge daylily clumps growing in my garden that started with just one tiny proliferation! It's also a fun way to share plants with friends.
When I find a proliferation I cut the scape off of the plant and place it in a plastic cup of water to grow roots. I have found that the roots will grow quicker if you use a clear plastic cup (as opposed to an opaque one). Important: Be sure to keep the water in the cup clean. The roots generally grow large enough to plant in a week or two. I like to leave a good portion of the scape on both sides of the plant. When I eventually plant the proliferation in dirt, the scape gives the tender new daylily stability. The scape above the dirt will eventually dry up and fall off. I leave my proliferations in a pot for a few weeks to form roots, and from there I place it in the ground. In two or three years the proliferations pictured will bloom and look exactly like the beautiful 'Red Volunteer' pictured in the first photo.
I have grown 'Red Volunteer' ever since I can remember having daylilies. It is reliable, consistent, big, tall, and gorgeous. In addition to other awards, Red Volunteer won the 'Lenington All-American Award' in 2004, which goes to one daylily each year voted the best performer over a wide geographic area. This midseason, dormant tetraploid was hybridized by William Oakes and introduced in 1984. My plant grows 38" tall and the blooms are 7" or more in size. It is a definite wow! There will always be a place for Red Volunteer in my garden.