Ship integrity is a measure of the wear and tear to the ship's hull. 0% integrity effectively reduces your otherwise 100% repaired hull down to 70%.
Your hull health percentage shown under modules is relative to damage to the hull, say from a cannon or something. You have a hole in your ship or something has been blown off it, which can be repaired/replaced when you dock.
Your ship's integrity is the hull's condition in context of wear. You may have repaired all of your damage over the years or from your last few trips, but overtime things will need to be replaced due to end of useful life failures.
Someone runs into my car and knocks the bumper off. I go to the shop and they replace it and the tail lights, and now my car's "hull" is back to 100%, as all panels are in place and nothing is missing or broken. My car has 175,000 miles on it though, so I could probably stand to have all of the hoses and seals replaced before they fail (yeah, these things aren't in the "hull" of the car, but you get the point, and I really should get those done....)