Cargo class denotes the types of wares that a ship may, or may not, be able to carry. Not to be confused with ship equipment levels.
Each ware has a transport class (or cargo class) and takes up a specific amount of ship cargo-hold, for example one unit of Rastar Oil takes up 6 units of space in M class containers, a unit of Argnu Beef takes up 4 units in S class containers, and an Ore Mine takes 8000 units in ST class containers. Note that this also applies to weapons and shields (even when installed).
All together these wares would take up 8010 units of space on a TL class transport. TL to handle the ST cargo 8010 for the combined space.
Some types of equipment (e.g. jumpdrives) also have a minimum cargo class, and can only be installed on ships capable of transporting that class (although they don't actually take up any space).