Cargo expanders do what they claim; they expand the your cargo space. An (incomplete) list of all Cargo expanders is available in the cargo expanders category. Cargo expanders all have energy, skills and captain level requirements so always check before purchasing.
You can divide cargo expanders in four groups: basic cargo expanders, passenger cabins, recycling units, and rare loot expanders.
Basic Cargo Expanders
Cargo Expanders increase your cargo space. Most of these are purchased, though the Storm series is player made (and generally superior).
Click here for a list of the Common Cargo Expanders available for purchase in the Settlement shops.
Passenger cabins are cargo expanders that allow to you to transport passengers. Normal passenger cabins do not increase your cargo space. However, the Passenger ShadowSword Frame does increase your cargo space, but relies on pods to provide space for passengers.
Rare Loot expanders are cargo expanders that can be found while your participating in mining, salvaging, or combat. They pop up on your screen as an extra box at the bottom of the screen. There is no NPC shop to purchase them in so the only way the aquire these items is by finding them or purchasing them from fellow players.
Core-Exiles currently has five cargo expander vendors dotted throughout the known galaxies. Of course, many cargo expanders are player made, so for those cargo expanders you'll have to contact a crafter.