serve as illustrations (literally are being allegorized): In allegorical writing, every character and event symbolizes a deeper meaning. Allegorical interpretations often ignore the text's historical meaning and create imaginative meanings. Here, however, Paul understood the story in its historical context and saw it as history. But he interpreted the story's characters as symbols of the current situation. Paul's opponents were also using allegorical methods, so Paul countered their flawed allegory with true allegory (see 1 Corinthians 9:22).
two covenants: The old covenant (God's special agreement with his people) was formed through Moses. The new covenant came through Jesus Christ.
Mount Sinai… This is Hagar: Just as Hagar was a slave woman symbolizing human effort, Mount Sinai brought slavery to following the law.