"Hull Integrity" is intended to simulate the wear and tear of continuous operation - rivets rattling loose, welds developing microfine cracks, that sort of thing. Nothing lethal or fatal. Your ship won't explode or come apart at 0% Integrity. The generally quoted figure is that a ship with 0% hull integrity but no damage (100%) is equivalent to flying around with a hull at 70% damage. There has been speculation that low integrity also makes modules more vulnerable to damage; this was apparently discussed way back in alpha development but we don't know if it was ever implemented and attempts at testing it have shown no evidence.
And if you're wondering, since it hasn't been mentioned in this thread: it is Supercruise travel that causes both Hull Integrity and Paint Wear to decline, both at the same rate of 1% per 100,000 Ls travelled. You can prove this by making the pilgrimage to Hutton Orbital: if you begin the voyage at 100% and fly to Hutton in a straight line, your Paint and Integrity will both decline to 37%, meaning you've lost 63%. And Hutton is just under 6.4 million Ls away. Nothing else causes Integrity or Paint to fall: actually making hyperjumps between systems, taking damage in combat, flying through atmospheres, crashing into things, all these things do nothing to your Integrity levels. Supercruise travel alone causes the decay.
There is no way to measure Integrity directly while in flight; you can only see it when docked somewhere with repair facilities. If you are concerned about Integrity levels while out in the black where you can't get a precise reading on it, there is a way to guesstimate it. If you get in the habit of always repairing your Paint and Integrity at the same time, then, since they decay at the same rate, you can eyeball your paint wear and use that as a rough indication of your Integrity loss. You might need to "calibrate your eyeballs" for your specific ship type and paintjob, while flying around the Bubble, by watching your paint wear gradually develop, and seeing how that compares to the actual paint wear statistic. Of course, if you're one of those degenerates that actually likes to fly around with 0% paint all the time, then you can't use this method.
