When he discovered his home planet, Krypton, was becoming unstable and would soon perish, the scientist, Jor-El, built a rocket to transport a single Kryptonian off planet to another world.
After learning Krypton's time was just about up from Brainiac, Jor-El used the rocket to send his son, Kal-El, to Earth. He and his wife, Lara, recorded a message for their son to explain where he was from and why they had to send him away. They also made sure to explain the abilities he would gain under the Earth's yellow sun.
The ship successfully made its way to Earth (accompanied by what would become known as Kryptonite) and landed in the outskirts of Smallville, Kansas. Jonathan and Martha Kent discovered the ship and adopted Kal-El as their own son, Clark. They kept the ship in a large crate in their barn, but did not show it to Clark until he was a teenager and his abilities started to manifest.
Years later, after becoming Superman, Clark brought the ship to the Xavier Institute, where he repaired the ship and make some modifications to it so he could explore space. Along with a Nano-suit to survive in space, the Krypton - which Clark had named - was first launched in the middle of the Atlantic Ocean after being deployed from the Blackbird and traveled to Mars and Jupiter.