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The adapter, which costs $19 in the U.S. Apple Store (as opposed to £15 in the UK and €19 in rest of Europe), lets you connect an iPhone, iPad, or iPod with a Lightning connector to a Micro USB cable and use it to sync and charge your device.
Apple's Lightning connector is the new power connector used in the latest generation of iPod, iPad and iPhone devices. It replaced Apple's previous 30-pin dock connector, and is incompatible with cables and devices created for that connector.