King James (lived from 1566 to 1625) reigned as King James I of England from 1603 to 1625. In 1604, shortly after he took the throne, a delegation of Puritans (a strict group of English Protestants) met with the king at the Hampton Court Conference. They requested several things of him. Mostly, King James ridiculed them and rejected their requests. However, there was one notable exception. He liked their idea of a new translation of the English Bible and authorized this new translation.
Seven years later, in 1611, the new translation of the Bible into English was completed. It was commonly called the Authorized Version because of the authorization given by King James. But, being connected with King James so closely, it was often called the King James Version of the Bible. Over time, this name has become the most common name and many who love it dearly simply call it the King James Bible.