Once upon a time there was a Lamp. That Lamp was the Gospel. Then Christ came to teach the Gospel, perform the Atonement, and establish His church. The church Christ established is like a LampShade, it holds all the 'Light and Knowledge' of the Gospel.
However, after the Resurrection of Jesus Christ the church was persecuted, and the Apostles who received Priesthood Authority were killed. This means that the Lamp was broken, because no one had the Authority to direct Christ's Church.
Less than 500 years later there were a small number of churches that had pieces of the broken Lamp. People knew that something had been lost and they tried as best they could to reform the Lamp. Roughly 1000 years later there were many churches, or many Lamps, that all claimed to be the "True Lamp". That they each had part of that Lamp it is true, but none were the Lamp of the Gospel as it was supposed to be.
But even if the Lamp came close, the Lightbulb of Authority was still missing. You see Christ is the 'Light of the world', and so even if you have all the components of a functioning Lamp only when He puts in the Lightbulb does that church give Light.
The same Lamp of the Gospel, with the same church organization or LampShade, was once again found on the Earth. God gave the Authority of the Priesthood to Joseph Smith, who ordained others, and the Priesthood has never again left the Earth.