Purple Trillium, Red Trillium, Wake-robin, Stinking Benjamin and Birthroot are all names for the maroon to dark purple trillium (Trillium erectum) found in the spring woods.
This trillium's unpleasant odor and color of rotting flesh attracts pollinators such as carrion flies.
The seeds have large, oily elaiosomes (appendages rich in oil and proteins) that are attractive to ants. The ants bring the seeds back to the nest where they feed on the elaiosome and leave the seed to germinate. This use of ants as a means of seed dispersal is called myrmecochory.
The three, large green leaves are not leaves at all. Rather they are photosynthetic "bracts" (parts of the flower). In reality, trillium have no above ground leaves!
There is also a "white morph" of the purple trillium. It can be distinguished from other white trillium by the purple inner flower parts.
Picking any part of a trillium kills the plant. So best just looking at them in the wild!