Lily buds are the unfurled flowers of the Hemerocallis fulva (daylily). The flowers which are sometimes called "tiger lily buds" or "golden needles" (gum jum) hale from China. The buds are used in numerous Chinese traditional dishes but most prominently in "jai" or Hot and Sour Soup which is a dish prepared for pre New Years celebration. The buds look like long golden to darker brown strips. You can read more about edible flowers here.
Typically lily buds need to be rinsed in a colander under cool running water. Place the rinsed buds in about 2 cups of cool water and allow them to soak for about 30 minutes. Once the buds are hydrated you can drain them then snip off the tougher thick end and discard (hopefully compost). Some recipes might suggest you cut the strips in pieces but they look nice left long. Click here to learn more about lily buds.
What to substitute if you don't have lily buds? The texture and the flavor of lily buds is pretty difficult to reproduce but here is the best option:
Look for this product in a well-stocked Asian grocery store, otherwise you can buy them online at Amazon.com