Tartarus is both a primordial deity of the Underworld as well as an inescapable dungeon.
As a deity, Tartarus was third one in existence with Chaos (Void, dividing) and Gaia (Earth) preceding him. After him came Eros (Love, unification.)
As such, not much is known of him. Primordial deities weren't often presented as creatures. Mostly they were broad concepts who created Titans when they copulated.
As a place, Tartarus is a prison that is often referred to in Greek mythology. After War of the Heavens the Titans were imprisoned here. Before them, Titans had imprisoned Cyclops and Giants there. It's a place of punishment and suffering.
Geographically Tartarus is located far beneath the Underworld. The two share a link between them and Tartarus is often seen as a part of the Underworld. However, it precedes the Realm of Hades by a large margin.