From Destinypedia, the Destiny wiki
Asphodelia are a species of red flower native to the Black Garden. They are frequently referenced in lore entries referring to the Garden, sometimes seeming to be used as a metaphor for conflict. To the Awoken, they are a symbol of the fragility of life.
Asphodelia was introduced to the Dreaming City by Uldren Sov following his exploration of the Black Garden alongside Jolyon Till. They have lost, however, their vivid red color. The Awoken used to grow them to mark births and deaths, and it is taboo to pick them for any other reason. They apparently have "a unique power over an Awoken soul". Getting a thorn in one's skin could cause paranoia, violence and madness, but a tea with the petals steeped in it brings peace and enlightenment.