Daylily blossoms display typical lily flower structure, as described on our Lily page. In the picture above, the single white, slender object projecting into the top, right of the image is the style, with a tiny stigma at its tip. Along with the style, six stamens emerge from the flower's center. The picture at the left shows a cross section of the same flower. Here you can see that the ovary sits at the bottom of the slender, cylindrical corolla tube.
At the right you see a close-up of the ovary at the left. One neat thing about that picture is that it shows the ovary glistening with wetness. That wetness is sweet nectar. Seeing this, you can imagine a butterfly landing on the flower and inserting its long, strawlike proboscis down through the corolla tube, to the nectar at the very bottom.
In the picture at the left you can see that the stamens arise atop the corolla tube, not at the tube's bottom, where the ovary resides. At the right is a much magnified view of one of the six anthers, opening like a bag atop its slender filament. Of course the golden powder is pollen.
Many fancy horticultural strains of daylily have been developed from the eight or so horticultural species of the genus Hemerocallis -- the Daylily genus. For example one in my garden is shown below. This is a "double-flowered" specimen.
As we see on our Rose-Flower Page, the genetic information forming stamens is closely associated with the information that creates petals. Consequently, horticulturists have managed to breed flowers so that some or all stamens develop into colorful petals. As with the roses, sometimes it's possible to find structures in "double-flowered" blossoms that are part stamen, part petal. In the picture at the left, at the upper left, the inset shows such a strange thing. You see part of a brownish anther at the edge of what otherwise is clearly a petal!