Hull is the remaining life of your ship. Every ship starts with the maximum of 30 hull points. Whenever your shields are pierced and you take damage to any compartment (including an empty room), it lowers your hull count, as well as when any system is completely destroyed by fires or by boarding parties, in which case you lose 1 hull point. It is also possible to lose hull points as a direct result of random events. The Rock Plating augmentation has a 15% of negating any hull damage caused by a hit taken (it cannot prevent damage from fires, boarding parties, or events).
Hull points can be repaired by spending Scrap in a Store, using a Hull Repair Drone, or gradually with the Repair Arm augmentation. There are also random events that are capable of fixing the hull, either for a price (such as repair stations) or as a reward.