Hulls are the part of the ship that everything attaches to and are also responsible for keeping everything inside (crew included) from being blown out into space. Usually made of some kind of thick, strong material, they are also the last resort when it comes to stopping weapon fire after the shields (if any) are gone.
Hulls can only hold so much. Each component that a ship requires takes up an amount of space in the hull. Also, hulls can only take so much stress from engines and have ratings determining how large of an engine you can attach to it. After including engines, power sources, crew quarters, and all the various other parts, you may not have enough room for all the weapons you'd like. For these reasons, hulls are one of the main factors determining what a ship can do.
Hulls can be made out of many different materials, all with varying degrees of protection, mass, and cost.
Most hulls all share a common set of possible tweaks. See Common Hull Tweaks for more information.