After introducing us to a righteous priestly couple, Luke uses their story to demonstrate how he wants the reader of his Gospel to respond to all he's about to write - which is with faith. Zacharias receives good news that his barren wife will finally be given a son, yet he responds in unbelief, inciting the discipline of the Lord. On the other hand, his wife responds to the good news in a manner we ought to respond, which understanding God shows us undeserved favor. A great point is seen in Elizabeth's final statement - that God has removed her shame- a symbolic statement of what God has done for those who respond to the good news of Jesus Christ in faith.