Systems describe what a ship is capable of doing: how good its weapons are, how tough its hull is, how fast its engines are and how much room it has in its cargo hold. At Ship Construction each ship has 5 points that can be spent on its systems and each system can have a maximum of 3 points in it.
Remember: If your ship class comes with a 'Favoured System', it already has 1 point in that system. However, that system is still restricted to 3 points in total. Equally, if your ship class comes with a 'Penalty system', that system can never have points above 1. You still have 5 points to spend in either of these cases.
The Ship's cargo hold is where all fuel and large items are stored. This space is finite and cannot be exceeded: any excess items must be jettisoned into space else the ship will start to drift due to detected unsafe conditions of an overfull hold. In particular, the limit of three units of FTL Drive Fuel cannot be exceeded for safety reasons.
Engines are pivotal to moving a ship from A to B. Better engines make your ship go faster and make it more manoeuvrable too. These are distinct from the FTL Drive and do not use solid fuel to run.
The ship's hull is what protects its crew and its interior workings from the dark, empty void of space. It's what takes the beating in combat, in difficult environments or when entering atmospheres and the tougher the hull the better it will cope.
If there are two objects left in the universe, one of them is going to want to blow the other up. That's what weapons are for. The better a ship's weapons, the more damage they'll do if they hit.