Why do some door locks require the key to be twisted twice?
It's for security, making the lock harder to pick. About twice as hard. First you have to pick it to rotate the cylinder. Once it travels 360 back to the upright, the pins pop out from behind the rotatory sheath and must be re-picked to continue the final leg of the journey. With a key this is instant, but with a single-pin pick it doubles the (at least) the typical pick time. 

Depending on the mechanism (if the key is "stuck in" when unlocked "halfway") it can prevent bumpkey attacks as well since you can't pull back the bumper once the key is affixed. Some of what isherwood notes applies as well, tangentially, because high-security locks that have such a mechanism also have thicker/longer bolts and more robust mechanisms that require additional torque, compared to a crappy kwikset or schlage a residential customer might get at a box store.