(covers information from several alternate timelines)
On many Federation starships, the secondary hull (also known as the engineering hull, the engineering section, the stardrive section, or the battle section) was a major component of the overall hull structure. The secondary hull was generally located behind and below the primary hull.
The secondary hull was usually dedicated to engineering and support functions, especially in starships built after the mid-23rd century. It was the home of the warp drive, Main Engineering, and other engineering support systems. Separating these potentially dangerous systems from the majority of the crew, located in the primary hull, allows the secondary hull to be abandoned in the event of catastrophic damage to the warp core or a loss of antimatter containment.
The warp nacelles also make a direct connection to the secondary hull. Other areas typically found in the secondary hull include the shuttlebay, cargo bays, Crew quarters, corridor, transporter room and brig. The main deflector dish was usually located at the very front of the secondary hull, as were torpedo launchers.
On Galaxy-class starships, the secondary hull was usually referred to as the battle section because it mounted the majority of the ship's weaponry and was intended to enter combat or other dangerous situations following a saucer separation. The saucer module, containing the majority of the ship's crew (including civilians) could then retreat to safety. Both sections could operate without one another for long periods of time. Once the crisis was resolved, the two sections could reconnect. Because of this, the battle section was designed with duplicates of systems usually found only in the primary hull, including a battle bridge, captain's ready room, sickbay, crew quarters, corridor, transporter room, a computer core, and other mission-critical facilities. (TNG: "Encounter at Farpoint")
The deflector dish weapon used against the Borg by the USS Enterprise-D in 2367 required the entire forward half of the secondary hull to be evacuated due to radiation danger. (TNG: "The Best of Both Worlds")
In an alternate timeline, debris from the secondary hull of the USS Voyager was found in the 29th century following a temporal explosion which obliterated the Sol system and Earth. (VOY: "Future's End")