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, 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.
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 for fixing the hull, such as repair stations.