A fastback sedan is a two-box sedan, with continuous slope from the roof to the base of the decklid (trunk lid), but excludes the hatchback feature.
Marketing terminology is often misleading in this area - for example, Daimler AG incorrectly calls the Mercedes-Benz CLS-Class sedan a four-door coupé because its semi-fastback design tries to give the impression of a coupé.
Typically this design is chosen for its aerodynamic advantages. Automakers can no longer afford the penalty in fuel consumption produced by the traditional notchback three box form.