The Apple iPhone contains a flash drive, which, unlike the hard drives in most computers, contains no moving parts. With traditional hard drives in computers, the memory can be destroyed by contact with strong magnets. Refrigerator magnets are typically not strong enough to cause this type of damage, but an industrial strength magnet can. In comparison, the flash drives used in iPhones are not harmed by magnets.
Magnets in iPhone Cases
Many iPhone cases contain magnets that hold the flap closed. Other iPhone cases feature a magnet on the back that secures the iPhone to a belt attachment or to a stand, such as those used in cars to keep the phone within reach but hands-free. The magnets used as enclosures for iPhone cases are not strong enough to cause damage to most electronics. The stronger magnets used to hold an iPhone to a stand or belt attachment won't damage to the iPhone's storage components, but they may interfere with other components -- image stabilization, for example.
Magnets in iPhone Accessories
Certain iPhone camera accessories contain magnets. These camera accessories usually state they are "Made for the iPhone" and therefore safe for use with the device. Some users have reported problems caused by certain iPhone camera attachments that contain magnets -- specifically problems with the optical image stabilization. Using these attachments and accessories is at the user's risk, and damage caused by their use is unlikely to be covered by the AppleCare Plan.