What do you get if you added powdered root of asphodel to an infusion of wormwood?

Asphodel and wormwood make a sleeping potion so powerful it is known as the Draught of Living Death.



This question can also be perceived in a more metaphoric and symbolic manor.
When Snape first asks it to Harry it could be taken as a first hint that there was more to the relationship between himself and Harry's mother, Lily, as appears on the surface. Asphodel, a plant from the Lily Family, is associated in mythology with regret and the dead. Wormwood is a plant known for its bitterness.

Therefore Snape is telling us that he regrets Lily's death, and the bitterness of the knowledge that he holds himself responsible for it has made his life akin to a living death.