Merlin and King Uther made a deal so that if Merlin helped him marry Igraine he would give him Uther's first born son. Many years later when Arthur is born Merlin takes him away.
The king is later poisoned and the Archbishop is now the ruler. Merlin comes to him and says he knows who the rightful king is. So Merlin sets up a contest to prove it and a person must pull a sword from a stone.
Arthur's is given to a family and his adoptive brother Sir Kay(he is a knight) learns of the challenge to become king and so he tells Arthur "get my things" and they go to London.
Twenty years later
Arthur forgets Kay's sword so he goes to get one. He pulls the sword from the stone looking for a sword proving he is the rightful king.
Then Marlin comes and tells his dad and brother he is the king. Arthur then has to do it in front of the crowd of people and he does and becomes king.
He then becomes king and has to do it at every public event and holiday.