Hairtrigger:
Being raised a Witness, one of thousands of Protestant denominations that started from Luther's Reformation Movement around 1517AD, I had never heard of Apostolic Succession until my recent studies on the history of Christianity.
As the story goes, when Jesus was on Earth he directly appointed 12 Apostles. Judas Iscariot's death resulting in a vacancy. In the book of Acts the remaining 11 Apostles appoint Mathias to replace Judas. This is the first person to succeed an Apostle by appointment from previous Apostles. Later Paul and Timothy would be appointed.
Over the years, every time one of the Apostles died the remaining Apostles would literally lay hands on a person who was to be one of the next Apostles. This procedure continued over the centuries whenever a Pope or Bishop was appointed. Every person appointed could trace their lineage of appointing back to the original 12.