Unlocking - The process of modifying the iPhone's software to allow the phone to work on cell phone carriers other than the official carrier in a given country.
When a user unlocks their iPhone, they are able to use the iPhone on other networks that it's compatible with. Apple's iPhone business strategy has been to select one, or a handful of, official iPhone carriers in most countries and to not sell iPhones configured to work with other carriers. When an iPhone is unlocked, the user can decide what cell phone carrier they want to use the iPhone with.
Apple has generally sold unlocked, contract-free iPhones for full retail price (usually US$300-$400 above the price subsidized by phone carriers) some number of months after the debut of each iPhone model. When users unlock the phone, they don't have to pay full retail price - however, it's unusual to be able to buy an iPhone at the lower price of $199-$299 without a carrier subsidy. As a result, many users unlock iPhone models older than the most recent one.
In July 2010, the Library of Congress declared that users have the right to unlock their iPhones to work with carriers other than the official carrier.
Unlocking is closely related to jailbreaking.