Scout Ships are Kryptonian vehicles that were commissioned by the Kryptonian Explorer Guild during the period known as the Kryptonian Expansion, or known as the Great Age of Expansion. They were used to travel to new worlds and colonize them, with great machines called World Engines able to reshape the environment. A scout ship called Scout Ship 0344 is currently the base of operations of Superman, but it is also in the possession of S.T.A.R. Labs.
Scout ships were used by Kryptonians during the Kryptonian Expansion to travel to explore and settle on new planets for colonization. After the users arrived on new worlds, they would create outposts, using great machines called World Engines to reshape the environments of the planets to be inhabitable for them.
Kara Zor-El was among the Kryptonians who colonized on new worlds. When she was old enough, she joined the Kryptonian Explorer Guild to train as a pilot, and she succeeded. She had her own team and her own ship in the terraforming project and went away. 
Kryptonians began having a lack of resources on their new worlds, causing the outposts to be abandoned with only Kryptonian remains, including scout ships. This caused there to be careless mining of the planetary core, destroying the planet. There are still abandoned scout ships throughout the universe.
Before Kara Zor-El left Krypton on her ship Scout Ship 0344 with her team, a Kryptonian named Dev-Em went to prison for killing Kara's boyfriend Kell-Ur, but he escaped and hid in her ship, killing her team when they were asleep. When Kara woke up, she noticed Dev-Em on the ship and her crew members dead, and the two fought, causing the ship to land on Ellesmere Island, Canada on the planet Earth. Because of yellow sun radiation on the planet, the two Kryptonians gained new powers. The fight ended when Kara killed Dev-Em, and abandoning the planet and Scout Ship 0344, causing the ship to freeze in ice.
Much later in 2013, the ship was discovered by Clark Kent, known as Superman, a Kryptonian raised on Earth after Krypton was destroyed. While in the ship, Clark met his biological father Jor-El's consciousness and he explained to Clark about what he was, what Clark was, and the history of the Kryptonian race, and teached him how to use his powers. The Scout Ship 0344 became known as the Fortress of Solitude, and became the base of operations of Superman.
Later in Metropolis, Lex Luthor entered the Genesis Chamber of the ship in an attempt to create the Kryptonian mutant Doomsday to kill Superman. Superman later arrived at the ship to stop him, but he was too late and Lex unleashed Doomsday, and he killed him but Doomsday failed to live. Lex was arrested soon after he contacted a New God named Steppenwolf on the ship.