Newer models of the iPad, iPhone, and iPod touch use the Lightning connector instead of the old 30-pin dock connectors. The Lightning connector is smaller and you don't have to worry about inserting it upside-down, so on the whole this is a good change. However, the connector plug is not as sturdy as the old plug, and my wife somehow broke the plug off inside her iPad.
It is pretty easy to pull a broken plug out:
- Get a small screwdriver (small enough that the head will fit in the Lightning port)
- Put a small drop of super glue on the tip of the screwdriver
- Insert the screwdriver into the socket and hold it against the broken plug. Be careful not to touch the sides of the socket with the super glue.
- Wait about 30 seconds for the glue to set.
- Pull it out smoothly. The Lightning plug isn't held with much force, so this should be easy.
Unfortunately, there is no way to repair the cable, so you'll have to go to your friendly neighborhood Apple Store and give them twenty bucks for a new one.