Weepwood Flowers grow on Weepwood-trees amongst Weepwood Leaves in Swamplands, mainly on top of the trees. These flowers have the shape of cubic blocks and glow faintly in the dark, which makes them more easily to find when it's dark.
These flowers can be used for crafting Poison Bombs in your Crafting Menu opened with "q" as the default key (or at any Crafting Table in older worlds).
Weepwood Flowers can also be used as an ingredient in Basic Health Potions, Stone Mining Cells, Taming Collars, Golden Potions and Stamina Regeneration Potions - in crafting-recipes that will accept any kind of Flowers. They glow very faintly, so they cannot really be used as a light-source.
On top of these flower-blocks Mossy Leafies can occasionally spawn, perhaps rarely other creatures too. At night / in darkness Night Leafies might spawn, even if the flowers were placed as an additional decoration inside a house made of crafted blocks.
Weepwood-trees cannot be grown from Saplings as of yet (R26 in December 2015).
A method to get more Weepwood Flowers is to place blocks of Weepwood Flowers on the ground and pick them up again - once in a while you will obtain 2 flowers at once when doing that.