The Greek Arabia (Ἀραβία) refers to the region of Arabia — broadly the great peninsula between the Red Sea and the Persian Gulf, and more specifically the Nabataean kingdom to the east and south of Israel. In the New Testament it appears in Galatians 1:17 where Paul describes his retreat to Arabia after his Damascus Road conversion, and in Galatians 4:25 where it is used in the Hagar/Sarah allegory.
Paul's retreat to Arabia after his Damascus conversion (Gal 1:17) is one of the most theologically intriguing silences in his autobiography. The desert of Arabia — the wilderness east of Damascus — was where Paul spent an unknown period before returning to Damascus. Arabia was his wilderness formation. Just as Moses spent 40 years in the wilderness of Midian before leading Israel, Paul was shaped in the silence of Arabia before his apostolic ministry. In Galatians 4:25, Arabia becomes the symbol of the Sinai covenant of law and bondage — contrasted with the Jerusalem above, which is free. For Paul, the geography carried the theology: Arabia-Sinai is slavery; the heavenly Jerusalem is freedom.