Answer: What you are observing are seed pods. Typically the spent flowers are snapped off before seed pods form. This will result in additional flower production on the flower stem. While you can allow the seeds to mature, there's no guarantee that they will be viable. And, daylilies are so easy to divide to produce a new clump that I'm not sure it would be worth your effort to harvest the seeds. I'd snap the spent flowers off before they begin forming seed pods to redirect the plant's energy into producing more flowers.
Best wishes with your garden.
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