Pathos and Angst
A wraith's psyche feeds on Pathos, the energy of emotion. Each wraith has several Passions, the emotions which are most tightly connected to its personality. Experiencing these emotions, even vicariously, provides the psyche with energy that the wraith can then use for various purposes.

The Shadow also has energy, called Angst, which it can acquire by fulfilling its own passions. These Dark Passions are generally contrary to the wraith's own goals.

Lifecycle and Types of Wraiths
Wraith status is defined by a combination of age, maintenance of one's Fetters and Willpower. The lowest form of wraith is a Drone, a wraith that does not have any Willpower or personal identity, drones are condemned to eternally act out their personal tragedies and are tightly bound to their Passions and Fetters. Having no personality or self-will, they are usually converted into raw materials as soon as they are found.

Self-aware wraiths
When a wraith dies, it is reborn in the underworld covered in a layer of plasma called a caul. The caul keeps the wraith docile until it is removed, a few wraiths remove their cauls themselves, but the majority of cauls are removed by another wraith, traditionally called a Reaper.

Young wraiths are called Lemures, with the distinction between a young and an older wraith primarily being Fetters. A Domem is a wraith whose Fetters are all destroyed, preventing them from staying in the Shadowlands for any period of time - while Domemhood generally implies age, a wraith can become a Domem while still very young, all it requires is that their Fetters be destroyed. A Gaunt is an older wraith who has resolved one or more of his Fetters, and still maintains them. Gaunts are significantly more powerful (and generally more canny) than Domems, and are consequently more respected in wraithly society, though there are rare exceptions, such as the Deathlords.

The final distinct class of wraiths are Spectres, which are wraiths who have been absorbed by Oblivion. Spectres have their own society, and from the wraithly perspective are mostly hostile entities out to destory all other wraiths.

Physically, a wraith is a coherent body of plasma, the substance that makes up the majority of the underworld. Plasm is a nonmaterial  that the Wraith unconsciously shapes into a form resembling their living body. The wraith's Corpus, their body-equivalent, can be changed by soul forging, and has only a loose relationship to what we would think of as a body. Most wraiths are solid plasma - which is to say that if you chopped a wraith in two, you would find no internal organs, just a consistent mass of  throughout the body.

Wraithlike bodies are subject to their own distinct metaphysics, they obey local rules of gravity, but under certain conditions can pass through material things. Plasma can also be used to manufacture objects, and many of the items in wraith society are comprised of other wraiths.

The wraith mind is divided into two parts, the Psyche and Shadow. After death, the negative, self-loathing and self-defeating parts of a wraith's personality form a distinct archetypal personality of their own. This personality, the shadow, is in communion with the darker forces of the Labyrinth and serves as a constant foil and antagonist to the Psyche. The Psyche, in turn, is the wraith's original personality. Wraiths have a higher, positive, personality as well, usually termed the Eidolon. In the modern era, the eidolon is generally fairly weak, and most wraiths are only marginally aware that they have one.

For a wraith to exist in the first place, it must be bound to the living world by one or more Fetters. Fetters are objects or creatures in the living world to which the wraith is connected and this prevents it from passing on. Fetters are a mixed blessing for wraiths - allowing them to interact with the living world, but also binding them to it.
Looking at the episode "The Awakening" in which Sherry Woods dies,sparked my imagination and had to find out if she could possibly come back and haunt Drew. It would be fascinating if she did come back as a Wraith and all the consequences surrounding those circumstances would be fascinating.