The first few space missions can be done with a brand new ship but to complete later missions, you need to upgrade your ship. Just as you need to upgrade your equipment and your character's equipment to complete harder game content. In fact yo equip ship upgrades the same way you equip new gear on you or your companion. Press C to show your character sheet, then click the Ship tab at the bottom (if you are on a speeder you might need to dismount before you will see the ship tab).
The ship upgrade interface for a smuggler ship is shown to the right. Click on one of the components to view a detailed description below, including information on where to get the upgrade and in some cases, how to use it.