Being a Christian is a result of a deliberate, life-changing commitment to Jesus Christ. This involves turning away from our rebellion against God and asking him to forgive our sins. Hence “my Saviour”. After this commitment we do not live for ourselves but for him, according to his will and with his constant help - hence we call him “Lord”.
We make this commitment because we have come to believe in God: that he loves us just as we are; that he wants us to know him and love him; that Jesus can bridge the gap of sin between us and God; that life goes best when it’s lived his way. The remaining vows cover the life that follows on from that personal commitment.