According to hunter Martin Creaser they "crack open skulls and feed on brain juice". They can pass as human but their true form is revealed in a mirror.
In 5.11 Sam, Interrupted, the wraith is disguised as a nurse called Kara. It amplified a person's insanity to make the brain produce more chemicals like dopamine, which it likes to feed on. She feeds on the brain through a thin pointed protrusion that emerges from her wrist which she inserts into the brain.
Wraiths can be killed with Silver