A wraith's Corpus is his equivalent of a body, comprised of a material termed plasm. In its default state, a Corpus resembles the body of the wraith at the time he died, often marked with whatever wounds led to his death as well as additional Deathmarks.
The corpus is highly malleable, however, and via the Moliate Arcanos, can be resculpted into nearly any form imaginable. That said, once changed, Corpora generally doesn't change back, and there are effects which can permanently mar a Corpus - some forms of damage are permanent, certain items embedded in the Corpus (such as living chains) permanently occupy Corpus until removed, and markings from them are often permanent and unmaskable.