Shadows are a type of monsters that only appeared in Disgaea: Hour of Darkness. They are essentially stronger and sturdier versions of Spirits. They use mainly fire and ice elemental spells.
It appears that this monster was replaced by the Reaper class as of Disgaea 3: Absence of Justice, as, despite their visual dis-similarities, they are both sturdy, magic-casting, end-game monsters. Furthermore, in Disgaea 1 Complete, the Shadow class was replaced by the Reaper class.
One of their most important appearances in the game is in Episode 8, where they are seen leading the Prinnies' souls into the Red Moon.